Theresa May has agreed the text of a Brexit divorce deal after all-night talks with European Commission President Jean-Claude Juncker, the DUP, and the Irish government, – foreign media say.

British Prime Minister made a series of calls to the Irish Taoiseach Leo Varadkar and the leader of the DUP, Arlene Foster, before finally agreeing on a compromise position on the Northern Ireland border.

She then travelled with Brexit secretary David Davis to Brussels for early morning talks with the Commission, before the deal was made and published by the EU. “I believe we have now made the breakthrough we needed,” Juncker said in a joint press conference with May, saying that “sufficient progress” had been made on Northern Ireland, Britain’s divorce deal and EU citizens, in order to allow the next stage of talks on Britain’s future relationship with the EU to begin.

He said that May had negotiated in a “generous” manner and made “significant commitments” on all of the three main issues that were up for negotiation. He added: “I will always be sad [about Brexit] but we must now start looking to the future.”

May said the talks had been “difficult” for both sides. “Getting to this point has required give and take on both sides,” May said. She added: “I very much welcome the prospect of moving ahead to the next phase to talk about trade and security and to discuss the positive and ambitious future relationship that is in all of our interests.”

May said there would be no hard border between Northern Ireland and the Republic or one between mainland UK and Northern Ireland and said she believed they had been able to secure an agreement on this.

However, the text of the deal states that if there is no formal Brexit deal the UK will ensure that “no regulatory barriers” will be created between Northern Ireland and the Republic, leaving the door open for continued alignment with the single market.

An agreement had been expected earlier in the week but was effectively vetoed by the DUP after the original version of the text suggested there would be continued “regulatory alignment” between Northern Ireland and the Republic.