Europe is demanding a quick resolution to the Withdrawal Agreement to allow the negotiation of a new trade agreement with Britain.
Reacting to Prime Minister Boris Johnson's decisive victory, European Union leaders said they are hoping for a quick British parliament vote on Britain's withdrawal.
Taoiseach Leo Varadkar said it was a positive thing that the election delivered a clear and decisive outcome.
“First of all, I want to congratulate, Mr. Johnson it's an enormous victory for him on a personal level, and also very clear result for his party,” he said.
“I think it's a positive thing that we have the decisive outcome in Britain in their elections.” Mr Varadkar added.
“We had for a few years of Parliament stuff wasn't able to form a majority around anything.
"We now clearly have a majority in the House of Commons to ratify the Withdrawal Agreement,” the Taoiseach told reporters.
European Council President, Charles Michel, extended his congratulations to Mr Johnson and also said the EU was ready to negotiate a free-trade agreement with Britain but called on the British government to work in good faith.
"We expect, as soon as possible, a the vote by the British parliament ... It's important to have clarity, as soon as possible," Mr Michel said.
"We are ready," he said of trade talks.
EU leaders are expected to put in motion preparations for the negotiations on the future relationship between Britain and the EU, which will begin soon after the UK leaves.
New European Commission president Ursula von der Leyen also expressed her desire to move quickly to strike a deal with Mr Johnson's government.
"We are all set," said, whose powerful executive arm negotiates trade deals on behalf of EU member countries. The commission also supervised the Brexit talks.
"We have the structures internally. We are ready to negotiate whatever is necessary," she said.
Asked whether it is possible to seal a trade deal in under a year, Mr Michel said: "It is not my intention to predict based on the experience of the past."
The European Parliament's Brexit co-ordinator Guy Verhofstadt tweeted: "Brexit will now happen. The British people have confirmed their referendum decision of 2016.
"The EU must now focus on building a new close, fair and lasting partnership with Britain. It is in our common interest."
Internal Markets Commissioner, Thierry Breton, said Britain's post-Brexit phase will begin on February 1st as Mr Johnson clearly has the ability to get the Withdrawal Agreement through the House of Commons.
"Boris Johnson will have a large majority... It seems logical to consider that (Johnson's Brexit deal with the EU) will be accepted by parliament, and therefore withdrawal on January 31st, which means we will be in the post-Brexit phase from February 1st," Mr Breton, a Frenchman, said on French radio RTL.
"The Brexit negotiations are over now. We are now entering a phase of trade talks between Britain and the EU."