Irish Prime Minister Leo Varadkar said Dublin had "achieved all that we set out to achieve" in phase one but added it would remain "vigilant"
Here are some of the reactions:
Irish Prime Minister Leo Varadkar said Dublin had "achieved all that we set out to achieve" in phase one but added it would remain "vigilant" in upcoming negotiations on post-Brexit UK-EU trade ties.
"This is not the end but it is the end of the beginning and we will remain fully engaged and vigilant through phase 2," he said.
And Foreign Minister Simon Coveney said the deal "fully" protected the 1998 Good Friday peace agreement and was a "very good outcome for everyone on the island of Ireland".
Even Northern Ireland's Democratic Unionist Party, which blocked a previous version of the agreement on Monday, said it was "pleased" to see some changes which meant there would be no "red line" between Northern Ireland and the rest of Britain.
"I think that the work which has been done in the negotiations that were initiated by Juncker and implemented by Michel Barnier has gradually resulted in common sense," French Foreign Minister Jean-Yves Le Drian told France Inter radio.
"We wanted the conditions of the withdrawal to be very clearly defined so that we can move to another phase and that's what's going to happen now, I hope."
"Very positive that the UK and the EU have taken this important step in the Brexit negotiations. An orderly Brexit is good for Europe and good for Norway," Norway's EU and EEA Minister Marit Berger Rosland wrote on Twitter.
Although it does not belong to the EU, Norway has access to the single market through its membership of the European Economic Area (EEA).
"Today's progress in EU/UK #Brexit negotiations is good news. Expect #EUCO can conclude 'sufficient progress' next week. Then we are ready to move to phase 2. #eupol #dkpol," wrote Danish Prime Minister Lars Lokke Rasmussen on Twitter, referring to the European Council.
Italian Minister of Economic Development Carlo Calenda hailed the move as "a major opportunity for Europe to recover" as it emerged from a "period of uncertainty".
Still, he said, Britain's exit from the EU is "a pity".
The move was also hailed in Berlin.
"It’s a step forward and now we will review the report" of the EU negotiators to see "if the conditions exist to move from phase 1 to phase 2," said Steffen Seibert, spokesman for German Chancellor Angela Merkel.
But the deal drew sharp criticism from hardliners back in the UK such as Nigel Farage, former leader of the UK Independence Party and a major driving force behind last year's Brexit referendum.
"It's not Brexit," he told BBC radio.
"A deal in Brussels is good news for Mrs May as we can now move on to the next stage of humiliation," he added on Twitter.
And campaign group Leave.EU called the agreement a "complete capitulation", saying: "Our lily-livered politicians have sold the country down the river".