Earlier on Friday, Spanish officials in Brussels said Sanchez might not attend the summit if London fails to put into writing a promise that no future agreement between Britain and the European Union that applies to Gibraltar can be signed without first being negotiated on a bilateral basis with Spain.
"EU27 has endorsed the Withdrawal Agreement and Political Declaration on the future EU-UK relations", Tusk said after less than an hour of the leaders' summit.
May is struggling even to unite her ruling Conservatives, and Northern Irish parliamentary allies the Democratic Unionist Party, behind the plan. "It will protect the integrity of our United Kingdom and ensure that there will be no hard border between Northern Ireland and Ireland - so people can live their lives as they do now".
European Union diplomats and officials said there was still no clear breakthrough on Saturday morning, hours before some of the other leaders must set off for Brussels ahead of Sunday's breakfast summit - few will be happy if plans change.
"I am totally convinced this is the only deal possible".
She said she had always rejected the "counsel of despair" from those who believed a beneficial Brexit agreement could not be struck.
And "with Brexit settled" the United Kingdom will be able to focus on the economy, NHS, building homes and tackling the "burning injustices" in society, the Prime Minister added.
European Commission President Jean-Claude Juncker, right, greets British Prime Minister Theresa May at EU headquarters in Brussels, Nov. 24, 2018.
She said that the draft agreement raises constitutional questions that can't be ignored.
Spain threatened at the last minute to withdraw from the summit until it was given assurances over trade arrangements with Gibraltar - a British overseas territory with 30,000 residents.
"Those who think that, by rejecting the deal, they would get a better deal, will be disappointed", Juncker said.
"So I will take this deal back to the House of Commons confident we have achieved the best deal available and full of optimism about the future of our country".
Theresa May insisted the UK's position on Gibraltar "has not changed" after she was accused of caving in to Spanish demands ahead of Sunday's Brexit summit.
British Prime Minister Theresa May arrives for an European Union summit at the Europa building in Brussels, Sunday, Nov. 25, 2018. They also backed a 26-page document laying out their aims for future relations after Britain leaves on March 29.
It comes after Spanish Prime Minister Pedro Sanchez received assurances from the United Kingdom government over Gibraltar, and dropped his threat to boycott the summit, BBC reported on Saturday.
Chief Minister Fabian Picardo fired back at Spanish Prime Minister Pedro Sanchez on Saturday night, dismissing his claims that Spain had secured "historic" gains in its sovereignty aspirations over Gibraltar.
"I have just announced to the King that Spain has reached an agreement on Gibraltar", he told a news conference.
The 27 leaders of the bloc met without Prime Minister Theresa May to endorse the agreement, which sets the stage for Britain exit from the bloc on March 29. "The British people don't want to spend any more time arguing about Brexit", she said.
'The reality is that if we are to secure a better outcome than is now on offer, then the only option is to look beyond this current draft withdrawal agreement and work in the time ahead for an improved outcome'.
The small DUP has an outsize role because its support has been crucial to May's shaky government, which doesn't enjoy a majority in Parliament.
European Union leaders are set to give their seal of approval to May's Brexit deal at the summit on Sunday, which had been threatened by a diplomatic row with Madrid.
During a radio grilling from the public, Mrs May refused to rule out resigning as Prime Minister if her highly contentious Brexit divorce deal is voted down.More news: Multiple injured, suspect dead in Thanksgiving Day shooting at Riverchase Galleria