Update 10.23pm: Fine Gael's national executive has outlined the final plans for the leadership contest.
Nominations will close at 5pm on Saturday, candidates must be nominated by at least eight members of the Parliamentary Party and an Electoral College system will be used for the first time.
The four regional hustings will take place at the end of next week, with voting beginning on Monday the 29th of May and continuing until Thursday the 1st of June.
The Parliamentary Party will then vote on Friday the 2nd with the results being announced later that day
Update 9.20pm: It has been announced there will be four regional debates for the Fine Gael leadership before any votes are cast.
The debates will take place in Dublin, Carlow, Galway and Cork.
Update 7.30pm: Enda Kenny has paid tribute to 'close personal friend' Michael Noonan on Twitter.
Mr Kenny called Mr Noonan's contribution to the restoration of the Irish economy "extraordinary."
Michael Noonan's contribution to restoration of the Irish economy has been extraordinary. Above all else he remains a close personal friend.— Enda Kenny (@EndaKennyTD) May 18, 2017
Update 5.10pm: Fine Gael MEP Deirdre Clune believes Simon Coveney is the right man for the Fine Gael leadership job.
Ms Clune said: "His experience in Europe will stand to him very well, he's a leader for a changed world in Europe regarding Brexit.
"Relationships with the US are going to be important and I think he has the skills needed to lead us."
The Coveney camp also made a big play on his own admission that he had asked to be Minister for Housing in the midst of an unprecedented homelessness and housing crisis.
He set himself a deadline of the end of June to end the practice of putting up homeless families in long-term accommodation in hotels and B&Bs. There are still about 600 families in that position.
Health Minister Simon Harris said: "Simon Coveney certainly doesn't shirk challenges; he confronts them."
It comes as Leo Varadkar takes a significant lead over Mr Coveney on day one of the Fine Gael leadership campaign.
The Social Protection Minister has a significant lead, but a third of the Parliamentary Party has yet to declare and the members and councillors also have to have their say.
Update 3.43pm: A group of TDs and junior ministers have publicly backed Leo Varadkar, declaring that he is the best man to lead Fine Gael and be the next Taoiseach.
One of those, Helen McEntee, a junior minister, said: "Look at the fresh new approach he has taken to politics, look at how he interacts with people, look at his vision for a more forward-thinking and open Ireland.
"This country needs a leader for the 21st century and Leo is that person".
Speaking in Leinster House, the group of 12 said they wanted a fair competition and an "honest fight" during the leadership election race, writes Juno McEnroe of the Irish Examiner.
Their declaration for Mr Varadkar brings to 22 the number of parliamentary members backing the social protection minister as opposed the 17 TDs, senators and MEPs so far who have said they are backing housing minister Simon Coveney for the top job.
More names are expected to emerge this evening and tomorrow morning, after the party's national executive formally meets this evening to agree the ground rules for the two-week race.
Update 2.49pm: Leo Varadkar has launched his campaign website to become Fine Gael leader, but has yet to speak publicly.
The site says that his campaign will officially launch on Saturday.
Update 1.44pm: Housing Minister Simon Coveney has strongly hit back at claims he lacks charisma.
He was in sombre mood this morning at a Healthy Ireland launch at Dublin Castle which he attended alongside Health Minister SImon Harris and junior health minister Marcella Corcoran Kennedy, both of whom are supporting Housing Minister Simon Coveney's leadership bid.
Update 1.14pm: Junior Gaeltacht Minister Sean Kyne has backed Leo Varadkar to be the next Fine Gael leader and Taoiseach, writes Juno McEnroe of the Irish Examiner.
Speaking to the Irish Examiner, he said the Dublin West TD had superior qualities to fellow contender Simon Coveney to take over the party.
“He answers the questions straight, I don't think he obfuscates or messes around in that regard. People like that approach that he has shown over the years."
He also said he was best placed for the country, to create jobs for workers, for equality, transparency and was open to listening to all sides.
“I think he would be a better debater for the party, I think he is more inclusive to most parts of the country, he is more attentive to the views of councillors and TDs.”
Meanwhile, nine of the 19 Fine Gael senators in the upper house have declared support for Mr Varadkar in the race.
This will be a blow to the Coveney camp who had thought they had a large number if not most of the party senators were on their side.
Senators Paddy Burke, Ray Butler, Maria Byrne, Martin Conway, Frank Feighan, Maura Hopkins, Michelle Mulherin, Catherine Noone, Neale Richmond all insisted that Mr Varadkar was the "best man" to lead the party.
It has also emerged this afternoon that junior foreign affairs minister Joe McHugh is backing the Varadkar campaign.
More TDs are expected to declare for the Social Protection Minister during the afternoon.
Update 12.54pm: Education Minister Richard Bruton has announced he won't be running for the leadership, and will back Leo Varadkar.
Mr Bruton said: "I believe that he is decisive, he is reforming.
"He has great capacity to deliver and has shown a track record of doing that."
Update 12.37pm:Nine of the 19 Fine Gael Senators in the Seanad have publicly declared their support for Minister for Social Protection Leo Varadkar in the Fine Gael leadership contest, voting for which will take place on June 2.
Leo's Senators declare support https://t.co/cDdcEF5owA— McConnellDaniel (@McConnellDaniel) May 18, 2017
The Deputy Leader of Seanad Eireann, Senator Catherine Noone said she believed that Leo Varadkar was the best candidate to lead Fine Gael.
"I know he can increase support for the party and widen its electoral base. He's a strong leader in Government with executive experience across three departments. Leo is a conviction politician who has the courage to do what is right.
"He believes that the Seanad can and should play a more central role both in Government and in the Oireachtas."
The following Senators have publicly declared their support for Leo Varadkar; Sen. Paddy Burke, Sen. Ray Butler, Sen. Maria Byrne, Sen. Martin Conway, Sen. Frank Feighan, Sen. Maura Hopkins, Sen. Michelle Mulherin, Sen. Catherine Noone and Sen. Neale Richmond
The senators spoke to the press outside FG headquarters.
Update 12.17pm: Minister for Education Richard Bruton will not contest the Fine Gael leadership and endorses Leo Varadkar.
Elsewhere, the Minister of State for Housing and Urban Renewal has said he has been very clear in his support for Simon Coveney as next leader of the party.
On Today with Sean O'Rourke, Damien English said that Minister Coveney has much experience and can build the party for the future.
He said Minister Coveney wants to ensure that politics can deliver for people and for communities.
Deputy English said that Simon Coveney wants to deliver on the programme for government and has proven that he can work with all political parties.
"To me, he has the CV to be a leader and I think at this moment in time, the issue around Brexit and European experience is key. Simon has proven and has worked as an MEP; his work in defence and sending our troops and our forces out to the Mediterranean, but also as a man to take on a job.
"I've watched the man coming in, put teams of people together for whatever the issue is and taking on the big challenge, and then making progress, getting the job done and delivering. That's key."
Fine Gael MEP Brian Hayes has said he is supporting Leo Varadkar for leader.
Mr Hayes said: "I think he has all of the characteristics and strengths that you need to survive in Irish politics and I think he's ultimately the change candidate for the party.
"He has grown into a politician of some standing in recent years since his election and, I think, more than anything else he really appeals to a diverse Ireland; and Ireland that is rapidly changing and I think at him at the helm he will do very well.
"He gives that diverse appeal to us (Fine Gael) and he also appeals to a younger generation."
Update 12.03pm: Housing Minister Simon Coveney has officially launched his bid to become the next leader of Fine Gael.
Health Minister Simon Harris was one of the first cabinet members to declare his support for Mr Coveney.
Standing outside the party's HQ in the last few minutes he said he wanted to heal the divisions that have opened in Ireland over the last decade.
He has also unveiled his election posters and is filing his nomination papers.
The other expected candidate, Social Protection Minister Leo Varadkar has yet to speak to the press but will launch his campaign website later.
Minister Coveney is behind him in the polls so far.
"I want to lead a party and lead a country that can heal many of the divisions that have opened up over the last decade or so.
"Unfortunately politics in recent times has been about cynicism, has been about negativity, has been about dividing communities across Ireland and I want to be a Taoiseach that can change that - that can change the mood of a country and change the direction of politics in Ireland," he said.
Update 11.58am: Dr James Reilly has said he is quitting his role as Deputy Leader of Fine Gael.
He also said that he will support Simon Coveney in the leadership battle.
Update 11.54am: Michael Noonan has said he will not be seeking re-election at the next General Election.
He released a statement today saying that following the Taoiseach's announcement yesterday, he does not wish to be considered for Cabinet by his successor.
"I have been honoured to serve as Minister for Finance since March 2011 and have introduced 6 annual budgets and one supplementary budget.
"I believe now is a good time for a new Finance Minister to take up office. Ireland is the fastest growing economy in Europe, the budget is almost balanced and we are on the cusp of full employment.
"I will continue to carry out my duties as Minister for Finance until a successor is appointed," he said.
Minister Noonan said it was "a privilege".
Update 11.11am: Fianna Fáil leader, Micheál Martin, has said the ongoing issue of whether there would be a new leader of Fine Gael and when there would be a new leader has been a factor in retarding the Government's capacity to deliver.
On Today with Sean O'Rourke, he said he would like to think that there will now be a focus, but that remains to be seen.
Deputy Martin said that Fianna Fáil is prepared to honour its confidence and supply arrangement.
"I think it's reasonable that time and space is provided to get some action on certain key issues and prioritisation of key issues, but yes we will be watching that space very carefully to make sure that there is delivery and also a degree of generosity of spirit in terms of the implementation of the agreement between ourselves, Fine Gael and the Independent Alliance."
He also said that there was a lot of "angst" after the loss of so many seats in the last General Election and that Mr. Kenny was never given a chance to "settle".
The Irish Examiner understands Cork East TD and junior justice minister David Stanton, Mayo senator John O’Mahony, Kildare North TD Bernard Durkan, and Longford-Westmeath senator Gabrielle McFadden will back Mr Coveney today as the race to replace Mr Kenny officially begins.
East Galway TD Ciaran Cannon has declared his support for Leo Varadkar, as have Eoghan Murphy, John Paul Phelan and Michael D’Arcy.
Update 10.44am: Tanaiste and Justice Minister Frances Fitzgerald has this morning ruled herself out of the Fine Gael leadership contest, writes Daniel McConnell, Irish Examiner Political Editor.
In a statement released via her Twitter account, Mrs Fitzgerald who has endured a torrid time as minister in recent weeks, confirmed she would not be going forward as a contender to succeed Enda Kenny who resigned last night.
She said she was encouraged by the expressions of support from colleagues but concluded that “entering the contest is not the right decision for me”.
This morning, one of the main contenders, Housing Minister Simon Coveney is to launch his campaign outside Fine Gael Headquarters in Dublin.
Social Protection Minister Leo Varadkar is also due to launch his campaign later this afternoon and it is expected we will see a number of declarations of support for both men throughout the day.
Carlow TD Pat Deering, who is the vice-chairman of the party, this morning pledged his support for Mr Varadkar.
Update 10.10am: The Tánaiste and Justice Minister has ruled herself out of the Fine Gael leadership race.
Frances Fitzgerald says she did seriously consider it, was touched by the encouragement and support she received, but has decided entering the race is not the right decision for her.
Meanwhile nominations for the next leader have formally opened.
Housing Minister Simon Coveney will hand his in at Fine Gael headquarters this morning and launch a website.
Social Protection Minister Leo Varadkar is expected to reveal his campaign website later.
Earlier: Fine Gael's Rules Committee will meet today to lay out the plan for the election of a new leader.
The National Executive Council will decide when hustings and voting will take place around the country in order for the election to be concluded by June 2.
The two leading contenders, Leo Varadkar and Simon Coveney, will spend the day finalising their campaign launches, while speculation continues that a third candidate may emerge.
Parliamentary Party Chairman, deputy Martin Heydon says he cannot declare for any candidate.
"My role as referee is a very important one, and also as a member of the Ethics Committee, as part of Executive Council, my focus will be very much on the process and ensuring the process is done right.
"It would be completely inappropriate of me and I'd have to step down as chairman if I was to declare a preference for any candidate," he said.
Meanwhile, the Government Chief Whip says she will declare who she is supporting in the leadership battle today.
Regina Doherty says she expects Education Minister Richard Bruton will announce his entry into the race later.
At the moment Simon Coveney and Leo Varadkar are the front-runners in the race.
Deputy Doherty says she is confident the man she has chosen to support has the right stuff:
"You know what I just have the confidence in this person, so I'm comforted by the rest of the people that I know that share that confidence in this person.
"I'm looking forward to the competition over the next couple of weeks to set out and support what his vision is," she said.
As of midnight Enda Kenny vacated the office, with just 16 days of campaigning now getting underway.
That means the party can only today begin to officially draw up the plans for how he will be replaced.
It is believed candidates will have until Saturday to submit nominations, which have to be signed by eight TDs, senators or MEPs.
There will then be a series of regional debates around the country, and a final meeting of the parliamentary party in about two weeks time.
Each of those may also serve as a polling station, allowing the votes to be counted on the first or second of June.
Those votes are weighted in a complex system that gives the most decisive say to the parliamentary party ever, a system being used for the first time they were adopted in 2004, after being backed by a leader of Young Fine Gael named Leo Varadkar.
Fianna Fáil says a change of Fine Gael leadership won't affect how the country is run.
The party's Barry Cowen says they have no intention of doing anything that could lead to a snap election.
"Not on our say anyhow at this stage, as I've said to you we've signed an agreement committed to three budgets.
"We remain focused in working towards the provision of that budget, with an emphasis on the provision of public services similar to the last budget which had that emphasis three to one, which was a huge reversal to what had been pursued by previous Government," he said.
Fine Gael's long-time strategist Frank Flannery is predicting Leo Varadkar will take over from Enda Kenny.
Mr Flannery says favourites Simon Coveney and Leo Varadkar are both capable and interesting politicians, but predicts one is slightly ahead.
"Leo is probably standing out with some advantage and that will become clear in the coming days.
"He has been working hard at it and he's been focused.
"Simon has been working hard over the last couple of months and no doubt he's making ground," he said.