After 20 months of negotiations, the 27 leaders gave the deal their blessing after less than an hour’s discussion.
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.”
Labour, the Lib Dems, the SNP, the DUP and many Conservatives MPs are set to vote against.
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.
What has the EU decided?
- 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.
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.
PM’s message: ‘This is all there is’
It’s a compromise. It was always going to be. It’s not a happy compromise either.
People on both sides of the Brexit argument are already screaming their protests.
And although the prime minister must be relieved, she didn’t exactly say that she was pleased about the deal when I asked her at a news conference this lunchtime.
Instead, she said she was sure the country’s best days are ahead.
But however she really feels about it – and with this prime minister it is hard to tell – her strategy for the next couple of weeks is crystal clear.
Her case? This is all there is.
What was the mood in the room?
Around seven leaders spoke in the session of the 27 member states, mostly to say this was a sad day and they wanted the future relationship with the UK to be as close as possible.
After Mrs May’s address, roughly half of the leaders spoke. Several wished her good luck with the meaningful vote in Parliament.
No “what ifs” were discussed.
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.
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’s Andrew Marr that the UK was getting “between 70% and 80%” 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.
What are Mrs May’s critics saying?
Former Conservative leader Iain Duncan Smith said he would find it “very, very difficult” to support the agreement as it stood.
“I don’t believe that, so far, this deal delivers on what the British people really voted for,” he told Sky’s Sophy Ridge show. “I think it has ceded too much control.”
SNP leader Nicola Sturgeon – who wanted to stay in the EU – said it was a “bad deal” and Parliament should consider “better alternatives”, such as remaining in the single market and customs union permanently.
She told the BBC’s Andrew Marr show the agreement as it stood would leave Northern Ireland and the rest of the UK “still within European structures with no say in its rules”.
Former PM Tony Blair, who backs another referendum, said the deal was “a dodo”.