Theresa May and David Davis held meetings in Brussels
European Commission President Jean-Claude Juncker said "sufficient progress" has been made on the strict terms of the Brexit divorce.
He met with the British Prime Minister Theresa May and Brexit Secretary David Davis in Brussels - along with the European Union's chief Brexit negotiator, Michel Barnier.
Speaking in Brussels afterwards, Mr Juncker said: "I will not hide that in between Monday and this morning we had a lot of talks: the prime minister and myself, the Taoiseach and myself, the Taoiseach and the prime minister.
"That's the reason why I would like to that the prime minister for (their) determination.
"We discussed the joint report agreed by the two negotiators - Prime Minister May assured me that it has (the) backing of the UK government.
"On that basis I believe we have now made the breakthrough we need.
"Today's result is of course a compromise".
"Both sides had to listen to each other, adjust their position and show willingness to compromise."
In her remarks, Mrs May said: "In Northern Ireland we will guarantee there'll be no hard border, and we will uphold the Belfast Agreement.
"And in doing so, we will continue to preserve the constitutional and economic integrity of the United Kingdom".
"Getting to this point has required give and take on both sides.
"I very much welcome the prospect of moving ahead to the next phase to talks about trade and security, and to discuss the positive and ambitious future relationship that is in all of our interests".
The meeting followed talks that continued through the night between UK diplomats and Brussels officials aimed at resolving the Brexit dispute over the Irish border.
Mrs May's bid to clinch a deal eluded her on Monday when it was blocked by Northern Ireland's Democratic Unionist Party leader, Arlene Foster.
Amid a flurry of late-night diplomatic activity, Downing Street confirmed that Mrs May had spoken to Mr Juncker after he phoned the Taoiseach Leo Varadkar.
.@JunckerEU was on the phone with Taoiseach Leo Varadkar and then with @theresa_may. We are making progress but not yet fully there. Talks are continuing throughout the night. Early morning meeting possible with press/point thereafter. Tonight more than ever, stay tuned, gsms on.— Margaritis Schinas (@MargSchinas) December 7, 2017
A Government spokesperson said they achieved all their goals in phase 1 of the negotiations.
This includes preserving the Common Travel Area, protecting the Good Friday Agreement and, crucially, obtaining a guarantee that there will be no hard border.
Taoiseach Leo Varadkar, Tánaiste Simon Coveney and Minister for European Affairs Helen McEntee are due to speak at 8.00am.
In a tweet, Tánaiste Coveney said: "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."
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
The DUP - which is propping up Mrs May's government in London - objected earlier this week to what is known as "regulatory alignment" between Northern Ireland and the Republic, which the party claimed would mean maintaining a soft border and a new frontier with the UK mainland in the Irish Sea.
In response to Friday morning's announcement, DUP leader Arlene Foster said: "Upon receipt of the draft text on Monday, the Democratic Unionist Party indicated to the Prime Minister that we could not support it as a basis for moving forward.
"Since then we have intensely engaged with the government right up until the early hours of this morning to secure changes to the document, mindful of the significant issues at stake for the future of Northern Ireland and the United Kingdom as a whole.
"Throughout this process our guiding principle has been to act in the national interest to ensure the constitutional and economic integrity of the United Kingdom is not compromised as we leave the European Union.
"The Democratic Unionist Party has always been clear that the union that matters most to Northern Ireland is that of the union of the United Kingdom of Great Britain and Northern Ireland.
"As a consequence of the engagement between the government and our team, substantial positive progress has been made on improving the text of Monday's original draft paper."
According to a statement from the DUP, contained within the new text are commitments that:
But Mrs Foster said: "We believe there is still more work to be done to improve the paper.
"Specifically, more work is needed around the areas of cooperation where it would be necessary to have alignment of rules and standards, how any alignment could be effected without staying in the single market and customs union and what necessary alignment may be required to happen."
Time had been running out for Mrs May as she attempts to do a deal to allow leaders at the European Council summit on December 14th to declare "sufficient progress" has been made on divorce issues so trade talks can begin.