Britain has struck a 'divorce' deal with the EU, after frantic around-the clock negotiations tackled the knotty problem of the Irish border.
European Commission President Jean-Claude Juncker called it "the breakthrough we needed" allowing the two sides to begin discussions on crucial future trade and customs arrangements.
British Prime Minister Theresa May - who may have saved her job by getting the deal done - said it had required "give and take from both sides".
The Democratic Unionist Party, who scuppered a draft deal on Monday because they were concerned it would divide Northern Ireland from the rest of the UK, have cautiously accepted the new version, saying there was "more work to be done".
DUP support in Westminster is vital for May's minority government.
Under the deal, Britain will pay a financial settlement for outstanding debts and obligations, calculated and paid over time - and estimated in the media at about 50 billion euros.
It guarantees the continuation of current rights of the three million EU citizens in the UK to continue to live, work and study there, including family reunification rights for spouses, parents, children, grandparents and grandchildren.
And it guarantees there will be "no hard border" between Northern Ireland and the Republic, and also maintain the "constitutional and economic integrity of the United Kingdom."
The two sides always agreed there must be no hard border, in order to avoid a return to the "Troubles" and maintain the Good Friday peace agreement.
They were seeking a form of words that somehow did not lead the DUP to believe Northern Ireland's laws will diverge from the UK's, did not lead to differences in trade and customs regulations between north and south that would require border checks - but still allowed the UK to set its own trading rules separate to the EU's.
The end result was a hedge, rather than a solution to this problem.
The parties propose to solve it "through the overall EU-UK relationship", that is, in the coming trade talks.
If this isn't possible, the UK "will propose specific solutions to address the unique circumstances of the island of Ireland", the UK-EU agreement document says.
If there are no agreed solutions, the UK "will maintain full alignment with those rules of the Internal Market and the Customs Union" which are required to support north-south relations and the peace agreement.
This would be an unwelcome result, as May has repeatedly insisted that the UK would leave the single market and customs union as part of Brexit.
The deal also acknowledges that anyone born in Northern Ireland will after Brexit still be able to choose to be Irish, British or both.
Irish Prime Minister Leo Varadkar said the Northern Ireland solution was "politically bullet-proof".
He said Ireland would not exploit Brexit to push for a united Ireland, saying his government "has no hidden agenda".
The middle of next week is the last European Council meeting of the year: the last chance for the 'EU 27' countries to agree to proceed to Brexit stage two before a long winter hiatus.
