EU leaders have approved an agreement on the UK's withdrawal and future relations - insisting it is the "best and only deal possible".
After 20 months of negotiations, the 27 leaders gave the deal their blessing after less than an hour's discussion.
They said the deal - which needs to be approved by the UK Parliament - paved the way for an "orderly withdrawal".
Theresa May said the deal "delivered for the British people" and set the UK "on course for a prosperous future".
Speaking in Brussels, she urged both Leave and Remain voters to unite behind the agreement, insisting the British public "do not want to spend any more time arguing about Brexit".
The UK is scheduled to leave the EU on 29 March 2019.
The EU officially endorsed the terms of the UK's withdrawal during a short meeting, bringing to an end negotiations which began in March 2017.
European Commission President Jean-Claude Juncker said anyone in Britain who thought the bloc might offer improved terms if MPs rejected the deal would be "disappointed.
But European Council President Donald Tusk, who broke the news of the agreement on Twitter, said he would not speculate on what would happen in such a situation, saying: "I am not a fortune teller."
Ahead of us is the difficult process of ratification as well as further negotiations. But regardless of how it will end, one thing is certain: we will remain friends until the end of days, and one day longer. #Brexit— Donald Tusk (@eucopresident) November 25, 2018
The UK Parliament is expected to vote on the deal on 12 December, but its approval is far from guaranteed.
Labour, the Lib Dems, the SNP, the DUP and many Conservatives MPs are set to vote against.
Mrs May has appealed to the British public to get behind the agreement - saying that although it involved compromises, it was a "good deal that unlocks a bright future for the UK".
At a news conference in Brussels, she said the agreement would:
- end freedom of movement "in full and once and for all"
- protect the constitutional integrity of the UK, and
- ensure a return to "laws being made in our country by democratically elected politicians interpreted and enforced by British courts".
The agreement, she added, would not remove Gibraltar from the "UK family" - a reference to a last-minute wrangle with Spain over the territory.
The EU leaders have approved the two key Brexit documents:
- The EU withdrawal agreement: a 599-page, legally binding document setting out the terms of the UK's exit from the EU. It covers the UK's £39bn "divorce bill", citizens' rights and the Northern Ireland "backstop" - a way to keep the Irish border open, if trade talks stall
- The political declaration, which sets out what the UK and EU's relationship may be like after Brexit - outlining how things like UK-EU trade and security will work
There was no formal vote on Sunday, with the EU proceeding by consensus.
Mr Juncker said it was a "sad day" and no-one should be "raising champagne glasses" at the prospect of the UK leaving.
While it was not his place to tell MPs how to vote, he said they should bear in mind that "this is the best deal possible...this is the only deal possible".
His message was echoed by Irish Prime Minister Leo Varadkar who said "any other deal really only exists in people's imagination".
But Lithuanian President Dalia Grybauskaite suggested there were a number of possible outcomes if the UK Parliament rejected the deal, including an extension of the negotiations, or another referendum.
What happens next?
Mrs May will now need to persuade MPs in the UK Parliament to back it.
She is expected to spend the next fortnight travelling the country trying to sell the deal before a parliamentary vote in the second week of December.
If MPs reject the deal, a number of things could happen - including leaving with no deal, an attempt to renegotiate or a general election.
Foreign Secretary Jeremy Hunt said the parliamentary arithmetic was "looking challenging" and warned "nothing could be ruled out" if Mrs May lost the vote, including the government collapsing.
He told the BBC that the UK was getting "between 70 percent and 80 percent" of what it wanted, while the agreement "mitigated" most of the negative economic impacts.
Asked if the UK would be better off than if it stayed in, he said the country would not be "significantly worse or better off but it does mean we get our independence back".
The agreement will also have to go back to the European Council, where a majority of countries (20 out of 27 states) will need to vote for it.
It will also need to be ratified by the European Parliament, in a vote expected to take place in early 2019.