Prime Minister Theresa May has struck a last minute deal with the EU to move Brexit talks on to the next phase.
There will be no "hard border" in Ireland and EU citizens in the UK, and UK citizens in the EU, will see their rights protected.
European Commission President Jean-Claude Juncker said "the breakthrough we needed" had been achieved, after months of negotiations.
Talks on post-Brexit trade between the UK and EU can now go ahead.
Northern Ireland's Democratic Unionist Party, whose opposition on Monday led to talks breaking down, said there was still "more work to be done" and how it votes on the final deal "will depend on its contents". Mrs May depends on the party's support to win key votes in Westminster.
Speaking at an early morning press conference in Brussels, Mr Juncker said: "Today's result is of course a compromise."
Negotiations had been "difficult for both the UK and the EU", he added.
Theresa May said getting to this point had "required give and take from both sides".
What has been agreed?
The leader of the DUP Arlene Foster, said on Friday she was "pleased" to see changes which mean there is "no red line down the Irish Sea".
Irish Foreign Minister Simon Coveney said the latest deal was a "very good outcome for everyone on the island of Ireland".
By Laura Kuenssberg, BBC political editor
Theresa May has achieved what she wanted - the green light to move on. Had she not, she was in deep, deep political trouble.
But the 15 pages, described as a "personal success" for Theresa May by Donald Tusk in the last few minutes, give her what she needed for now.
There are additional guarantees for Northern Ireland and the border, but an undefined statement on "full alignment", if there is no big trade deal.
The implications of what "full alignment" will mean will still be fought over by the two wings of the Conservative Party.
The joint report states: "the UK will maintain full alignment with those rules of the Internal Market and the Customs Union which, now or in the future, support North-South cooperation, the all island economy and the protection of the 1998 Agreement."
What happens to the border between Northern Ireland and the Republic of Ireland had been among the key sticking points in Brexit negotiations.
On Monday, the DUP objected to draft plans drawn up by the UK and the EU.
With regard to EU citizens' rights, Mrs May said the agreement would guarantee the rights of three million EU citizens in the UK.
Their rights would "enshrined in UK law and enforced by British courts".
The rights of UK citizens living in the EU will also remain the same and the administration procedure for those concerned will be "cheap and simple", Mr Juncker added.
The UK, which is due to leave the EU in March 2019, has been keen to open talks on a new free trade deal as soon as possible.
The EU would only agree to discuss this when it judged that enough progress has been made on the "separation issues" - the "divorce bill", expat citizens' rights and the Northern Ireland border - that have been the subject of negotiations so far. There has been much pressure to try to settle the Northern Ireland border issue before EU leaders meet next week.
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