An agreement on the UK's withdrawal from the European Union and its future relations has been backed by EU leaders after 20 months of negotiations.
The 27 leaders gave it their backing after less than an hour's discussion in Brussels, saying it paved the way for the UK's "orderly withdrawal".
Mr Tusk signalled on Saturday the deal would be approved after Spain withdrew last-minute concerns over Gibraltar.
The deal needs to be approved by the UK Parliament, with many MPs opposed.
Mr Tusk, the president of the European Council, broke the news on Twitter.
It follows more than 18 months of negotiations between the two sides, which began when the UK triggered Article 50 in the wake of the 2016 referendum leave vote.
The UK is scheduled to leave the EU on 29 March 2019.
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What happens if MPs reject Brexit deal?
The UK Parliament is expected to vote on the deal in early December but its approval is by no means guaranteed. Labour, the Lib Dems, the SNP, the DUP and many Conservatives MPs are set to vote against.
Prime Minister Theresa May has appealed to the public to get behind the agreement, arguing it is the best deal she could have struck - and honours the result of the Brexit referendum.
While the rest of the EU wanted it settled as soon as possible, Lithuanian President Dalia Grybauskaite said there were a number of possible outcomes if the UK Parliament rejected the deal, including an extension of the negotiations or another referendum.
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The BBC's political editor Laura Kuenssberg said European leaders were making clear that while they were not happy about the UK's exit, this was the best and only deal on offer.
What has the EU decided?
The EU leaders have approved the two key Brexit documents:
The EU withdrawal agreement: a 585-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.
In a one-page document confirming its decision, the European Council said the deal would pave the way for the UK's "orderly withdrawal" and it wanted the "closest possible" relationship in the future.
Before the meeting, European Commission president Jean-Claude Juncker said the UK's departure was a "tragedy" for the EU, adding that there are "no smooth divorces".
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'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.