- * Both sides agree to protect the Good Friday Agreement and avoid a "hard border" between Northern Ireland and the Republic.
- * If there is no trade deal, the UK will maintain "full alignment" with single market and customs union rules that "support North-South co-operation, the all-island economy and the protection of the 1998 Agreement".
- * If there is no deal, the UK will ensure that no new regulatory barriers develop between Northern Ireland and the mainland and that businesses in the province continue to enjoy "unfettered access" to the UK internal market.
- * Right for all Northern Irish people to take British or Irish nationality is preserved.
- * Common Travel Area to continue to operate.
Sinn Fein has given a "cautious and qualified" welcome to the agreement on the Irish border post-Brexit.
Party president Gerry Adams said many questions remained without answer.
"Brexit is the greatest threat to the economies of this island in generations," he said in Dublin.
"Today's communique does not set the final deal on Brexit.
"The communique sets out broad principles. These have been assessed by the Irish government as sufficient progress to allow the Brexit process to move into the next phase of negotiations on trade.
"While the communique recognises the unique and special circumstances surrounding the issue of the Irish peace process, the Good Friday Agreement and the border, it does not address key areas of concern for many citizens - especially nationalists living in the north and citizens in the border region.
"The insistence by the British that Britain and the north must leave the customs union and the single market presents a real and live danger which cannot be understated.
"This also contradicts the British Prime Minister's claim that there will not be a hard economic border.
Mr Adams said he had concern at the suggestion Northern Ireland would no longer be subject the jurisdiction of the European Court of Justice.
He added: "While today's communique represents some progress there are many unanswered questions around key issues and the Irish government must remain focused and vigilant.
"Sinn Fein is also very mindful that this Brexit process is a work in progress.
"Our experience through years of agreements with Britain is that the devil is in the detail."
Fermanagh farmer John Sheridan, who had planned to close his family farms amid concerns of a hard Brexit border, said they have now been granted "a stay of execution" by Friday's deal between the European Union and the UK.
"We had a lot riding on this. I was planning to advise the company, which is run by my children, to sell the stock and pull out. We have a stay of execution now.
"We had full intentions of starting the process of pulling the farms out. But now, I will certainly be saying I am happy to battle on," said Mr Sheridan, whose farms are on the south-west Fermanagh border.
"The border is all around me at a 90 degree angle. We wouldn't appreciate being held at a 90 degree angle when all our lives have been used to 360 degrees freedom.
Pro-Brexit farmer Robert Moore, who owns a beef and cereal farm on the border between Derry and Donegal, said it would have been "crazy" to put barriers up to hinder cross-border trade.
"There's a huge amount of trade that goes backwards and forwards across the border.
"Although I voted to leave, and that was primarily because I don't think the Common Agricultural Policy is delivering for agriculture, at the same time we still need to continue to trade. It is in everyone's best interests to continue to do that," said Mr Moore.
He added: "There is a huge amount of beef sold from southern Ireland into British supermarkets and we have a big market for our lamb in France for instance. Both sides would want that to continue, therefore there was always going to be a deal."
Coleraine farmer William Taylor, co-ordinator of Farmers For Action (FFA) NI group, said while he welcomed the announcement, a lot of work remained to be done.
He said that while the FFA would have preferred to have stayed in the EU, or within the customs union and single market regulatory alignment, Friday's statement of no borders "will be a good third option until we see how events play out between now and March 2019".
"Meanwhile, we expect to see Northern Ireland's politicians stepping up to the plate and getting back into Stormont immediately as there is work to be done including legislation on farm gate prices for the sake of Northern Ireland's prosperity and the certainty and sustainability for all of Northern Ireland's farming families and related industries," added Mr Taylor.
Paragraphs 49 & 50 from Brexit Deal are key for NI pic.twitter.com/ZSkDImo6xK— Mark Devenport (@markdevenport) December 8, 2017
The business community has also welcomed the the Brexit deal.
"It is definitely positive news. I must say I am relieved," said Sinead McLaughlin, Chief Executive of Derry Chamber of Commerce.
"There are a lot of guarantees in (the deal) for businesses here in Northern Ireland regarding North/South business and East/West business, so as a business community we are relieved that we have got through phase one," said Ms McLaughlin.
She added: "I am sure the next phase will be tricky enough, but the best case scenario for us at the moment is the guarantee there will be no hard border on the island or between Ireland and the UK and that's a guarantee if all else fails."
Toni Forrester, chief executive of Letterkenny Chamber, said she "cautiously welcomed" the border commitments, but warned a lot of detail remained to be sorted.
"We welcome that it is now in writing that there will be no border, but we really need to see the detail in the next year and a half in terms of trade deals.
"I just hope the next round of negotiations works out for our border counties. The next bit around trade tariffs is probably even more important because that's how businesses will figure out what their goods will cost," she added.
The British Irish Chamber of Commerce director general John McGrane, said businesses "will be relieved by the commitment of the UK to avoid a hard border with Northern Ireland by maintaining full regulatory alignment with EU single market and customs union rules".
He warned however that to provide certainty for business, the specific details of what constituted "alignment" would need to be confirmed swiftly.
Responding to the joint report on the progress of Brexit negotiations the General Secretary of ICTU, Patricia King, said the many circles were still left to be squared and that workers must not pay the price of Brexit.
"The Irish Congress of Trade Unions notes the publication of the joint report from the negotiators of the EU and the UK on progress during Phase 1 of the negotiations for Brexit. This comprehensive report requires detailed analysis and consideration.
"Given there is now agreement to proceed to Phase 2, we acknowledge the clear commitments from all - in particular the UK - to avoiding any possible hard border on the island of Ireland.
Ms King went on to say the ocuntry's largest trade union body has consistently called for the full maintenance and implementation of the Good Friday/Belfast Agreement, including its commitments to human rights and equality, and have reiterated on every possible occasion that this agreement must be central to any negotiations.
"It remains an enabler not an inhibiter to a final agreement. It was important that the all parties to the text reaffirmed their support for this agreement.
"The view of Congress is, and remains, that the best and most logical way to avoid such a hard border is for the UK as a whole to remain in both the single market and customs union. Our colleagues in the TUC fully concur with this view, as indeed do the majority of the business community on these islands.
"We do not want a harder border on the island of Ireland, nor an economic border with the UK east and west, nor between these islands. It seems to us that the text of this joint report also commits to this and Phase 2 of the negotiations can now commence. It is in this phase that the parties will have to square this circle," she pointed out.
Congress Assistant General Secrerary Owen Reidy went on to say it was essential that the Irish government continued to listen to the voice of the trade union movement on this matter and that the UK government starts to listen to the voice of the trade union movement, both through the ICTU in Northern Ireland and the TUC in the rest of the UK.
"We have stated from outset that workers must not pay the price of Brexit. There is some way to go in these negotiations and there will be many hurdles to cross. However, we insist that the voice of workers and their interests are heard and heeded."
The UK and the EU's joint commitment to the retention of a free-flowing Irish border post-Brexit is "rock solid and cast iron", the Taoiseach has said.
Leo Varadkar described assurances outlined in the agreed text as "politically bulletproof".
"We have protected what we sought to protect and we achieved what we sought to achieve," he said.
Reacting to the breakthrough at Government Buildings in Dublin, the Fine Gael leader downplayed changes in the wording of the text from Monday's ill-fated draft, which was scuppered by the Democratic Unionists.
He said the amendments were "stylistic changes in language" or "just statements of fact" that his government had "no difficulty with".
The Taoiseach acknowledged relations between the UK and Ireland had become strained during the phase one negotiations but he predicted that now his government has achieved the desired guarantees on the border it would become one of London's "closest friends" in the next stage of the Brexit talks.
In regard to the ratification of a potential final Brexit deal, Mr Varadkar said he did not think it would require a referendum in Ireland.
The Taoiseach said Friday's phase one agreement marked a "very significant day" for Ireland.
"This is not the end, but it is the end of the beginning," he added.
"And we will remain fully engaged and vigilant throughout phase two, the drafting and ratification of the new treaties that will be required between the EU and UK and their implementation."
Mr Varadkar said the UK's commitment to maintain regulatory alignment with the EU on cross-border issues was welcome, but he stressed that was a "backstop" position and the desire of London, Dublin and Brussels was a wide-ranging trade deal that would enable free access between Ireland and the whole of the UK.
Mr Varadkar hailed the commitment to avoid any controls, checkpoints or infrastructure on the border.
He said the deal had protected the Good Friday Agreement and the rights of people in Northern Ireland to be Irish, and therefore EU, citizens.
Mr Varadkar said the century-old Common Travel Area would be maintained and citizens of each nation would continue to have "freedom to live, work, study, access housing, healthcare, pensions and welfare" in each country.
He also welcomed the continuance of EU peace funding for communities on both sides of the border until at least 2021.
The Taoiseach said the deal was good news for all the people of Northern Ireland, and tried to assure unionists that he and his government did not have a "hidden agenda".
"There is no question of us exploiting Brexit as a means of moving to a united Ireland without consent," he said.
"We do not want to see a border in the Irish Sea, any more than we want to see a border between Newry and Dundalk or between Letterkenny and Derry.
"We want to build bridges, not borders.
"We want free travel and free trade to continue as it does now and has done for 20 years. We want reconciliation and respect to grow.
"Our guiding light - and our only ambition throughout - has been to ensure that the provisions of the Good Friday Agreement continue to operate in full after Brexit, and that people can go about their normal lives and business as before."
He told nationalists living north of the border that the Irish government had ensured their rights had been protected.
"There will be no hard border on our island," he told them. "You will never again be left behind by an Irish government."
Mr Varadkar thanked fellow EU states for the solidarity shown to Ireland in the talks.
"It is the clearest possible illustration of the values of the European Union and why small countries are better off in a big union," he said.
"It puts beyond any doubt that our future lies in the European Union at the heart of the common European home that we helped to build."
Tanaiste Simon Coveney said the retention of a specific Irish stream in phase two of the negotiations was a recognition that Ireland was the "most exposed and most vulnerable" of the remaining EU nation states to Brexit.
"I suppose there's an irony in the fact that the result that we want after all of these negotiations is as close to the status quo as possible, but that is what we want," he said.
The Democratic Unionists have welcomed the "substantial progress" achieved in the agreement between the UK and EU, but cautioned that much more work was needed on managing the Irish border post-Brexit.
DUP leader Arlene Foster said her party worked with the Government into the early hours of Friday to secure changes to the original text it rejected on Monday.
Mrs Foster said the North would now leave the single market and customs union and insisted there would be no border down the Irish sea, dividing Northern Ireland from the rest of the UK.
"There will be no so-called 'special status' for Northern Ireland as demanded by Sinn Fein," she said.
Mrs Foster added: "Northern Ireland will not be separated constitutionally, politically, economically or regulatory from the rest of the United Kingdom, and the joint UK-EU report at the conclusion of phase one makes clear that in all circumstances the United Kingdom will continue to ensure the same unfettered access for Northern Ireland's businesses to the whole of the UK internal market."
The DUP leader made clear there was "still more work to be done".
Taoiseach Leo Varadkar said it was a "significant day" for Ireland.
"We have achieved all that we set out to achieve in phase one of these negotiations," he told a press conference in Government Buildings in Dublin.
"I am satisfied that sufficient progress has now been made on Irish issues, the parameters have now been set and they are good."
He said Ireland's focus would now move to phase two of the negotiations. Mr Varadkar said his government would remain "fully engaged and vigilant" throughout the process.
"This is not the end but it is the end of the beginning," he said.
Mr Varadkar said he wanted to assure unionists of his motivations.
"There is no question of us trying to exploit Brexit to move toward Irish unity without consent," he said.
Tánaiste Simon Coveney said 'we have secured assurances' for all on the island of Ireland, ensuring no hard border, post-Brexit.
Deal Confirmed! Ireland supports Brexit negotiations moving to Phase 2 now that we have secured assurances for all on the island of Ireland - fully protecting GFA, peace process, all-Island economy and ensuring that there can be NO HARD BORDER on the Island of Ireland post Brexit— Simon Coveney (@simoncoveney) December 8, 2017
Speaking on RTÉ's Morning Ireland, Tánaiste Simon Coveney says "There is no scenario now in the context of Brexit that will result in a hard border".
"We want to assure people, north and south, that there will not be the re-emergence of border on the island of Ireland as an unintended consequence of Brexit," he said.
He said that they know now what the default position is and in absence of agreed solutions in Phase 2 there is a "fallback position".
He said: "What is being said is there is commitment in the absence of agreed solutions - in other words if there is no deal on a bigger deal that solves all these issues, well then there is commitment to maintain full alignment with the rules of the internal market and customs union.
"In other words that would be an arrangement accepted by the UK and the EU in this wording that will prevent any need for border checks, which is exactly what we are looking for.
"The default position is that the island of Ireland will maintain full alignment with Northern Ireland. There will be in no circumstances a need to introduce border checks on the border of Ireland."
Taoiseach Leo Varadkar and the Tánaiste are due to give an update shortly.
The European Commission has announced that "sufficient progress" has been made in the first phase of Brexit talks.
The announcement came after Theresa May and David Davis made an early-hours journey to Brussels to meet with European Commission President Jean-Claude Juncker and the European Union's chief Brexit negotiator Michel Barnier.
It followed talks which continued into the early hours between the Prime Minister and Democratic Unionist Party, Arlene Foster, whose party scuppered a deal at the eleventh hour on Monday.
Mrs Foster said that "substantial changes" to the text rejected on Monday would mean there was "no red line down the Irish Sea" in the form of a customs barrier between Northern Ireland and the rest of the UK.
Mr Juncker said that the decision on whether to move forward to talks on trade and the transition to a post-Brexit relationship was in the hands of the leaders of the 27 other EU nations, meeting in Brussels at a European Council summit on Thursday, but said he was "confident" they would do so.
The Commission president said: "I will always be sad about this development, but now we must start looking to the future, a future in which the UK will remain a close friend and ally."
Mrs May said that intensive talks over the past few days had delivered "a hard-won agreement in all our interests".
The British Prime Minister said that the agreement would guarantee the rights of three million EU citizens in the UK "enshrined in UK law and enforced by British courts".
She said that it included a financial settlement which was "fair to the British taxpayer" and a guarantee that there will be "no hard border" between Northern Ireland and the Republic, preserving the "constitutional and economic integrity of the United Kingdom".
She said that the agreement between the UK and the Commission, being published in a joint report, would offer "welcome certainty" to businesses.
Under the terms of the negotiations being carried out under Article 50 of the EU treaties, the European Council must agree that sufficient progress has been made on the divorce issues of citizens' rights, the Irish border and the UK's financial settlement before talks can move on to the issues of trade and transition.
The publication of the joint report makes it all but certain that EU27 leaders will approve this step on Thursday, marking a significant step forward in the process leading towards UK withdrawal in March 2019.
It eases pressure on Mrs May, who was facing the prospect of businesses activating contingency plans to move staff and activities out of the UK if no progress had been made by the end of the year.
Mr Juncker cautioned: "The joint report is not the withdrawal agreement. That agreement needs to be drafted by the negotiators on the basis we have agreed yesterday and today and then approved by the Council and ratified by the UK Parliament and European Parliament."
He said that he and Mrs May had discussed the need for a transition period following the formal date of Brexit, and shared "a joint vision of a deep and close partnership".
"It is crucial for us all that we continue working closely together on issues such as trade, research, security and others," he said.
"We will take things one step at a time, starting with next week's European Council, but today I am hopeful that we are all moving towards the second phase of these challenging negotiations and we can do this jointly on the basis of renewed trust, determination and with the perspective of a renewed friendship."
Mrs May said that the negotiation process "hasn't been easy for either side".
"When we met on Monday, we said a deal was within reach," said the PM. "What we have arrived at today represents a significant improvement."
Here is Theresa May's full statement on "six commitments to Northern Ireland".
: Theresa May and David Davis have arrived in Brussels to meet with European Commission President Jean-Claude Juncker and the European Union's chief Brexit negotiator Michel Barnier.
The Prime Minister and her Brexit Secretary arrived at the Berlaymont shortly before 7am Brussels time (6am GMT) on Friday morning.
The meeting follows a flurry of diplomacy by Mrs May late on Thursday that fuelled speculation that an agreement on plans to maintain a soft Irish border was edging closer.
A press conference is due to be held after the leaders meet.
In an apparent sign that a Brexit deal has been done, Mr Juncker's head of cabinet Martin Selmayr tweeted a photograph of white smoke gushing from the chimney of the Sistine Chapel - the traditional way of signalling that a new Pope has been chosen.
DUP leader Arlene Foster told Sky News her party had been "negotiating directly with the Prime Minister" into the early hours of Friday morning and received "very clear confirmation that the entirety of the UK is leaving the EU, leaving the single market, leaving the customs union".
Mrs Foster said that the PM "now has a text she feels she wants to take back to Europe", adding that it included "substantial changes" to the proposals which were rejected by the DUP on Monday.
"We think that there have been substantial changes made to that text since Monday," said Mrs Foster.
"As you know, on Monday we were unhappy with the text when we received it in late morning. We felt there wasn't enough clarity, particularly round the very important issue of access to the GB market.
"There have been changes right throughout the text and we believe there have been six substantive changes.
"For me it means there's no red line down the Irish Sea.