Dutch Prime Minister Mark Rutte, whose country is one of Britain's closest trading partners, praised May's handling of the hard negotiations and said he was confident that she could see the deal through parliament in the coming weeks.
The agreement had appeared at risk in the days leading up to the summit, when Spain's prime minister, Pedro Sánchez, threatened to withhold support unless Britain conceded that the British overseas territory of Gibraltar, over which the Spanish have a long-running territorial claim, would be covered by a future trade deal only with Madrid's consent.
It could refer back to the EU's 2017 Brexit mandate, which said that, after Brexit, "no agreement between the European Union and the United Kingdom may apply to the territory of Gibraltar without the agreement between ..."
The agreement takes the form of several declarations.
The British ambassador to the EU, Sir Tim Barrow, gave that commitment in a letter on Saturday afternoon, prompting outrage across the political spectrum by what was described as a "betrayal" of the Rock.
Gibraltar Rock is seen near the British overseas territory's border with Spain on November 15.
Then Britain issued a statement saying it would continue bilateral talks with Spain after Brexit on March 29 - and Sanchez relented.
The EU's chief negotiator Michel Barnier said the deal was a "necessary step" to prepare for the next phase of negotiations which the Government hopes will result in a wide-ranging free trade agreement.
The EU withdrawal agreement: a 585-page, legally binding document setting out the terms of the UK's exit from the EU.
"The European Council will therefore be held tomorrow".
Mary Kom, three other Indian boxers enter semi-finals
But I have to settle for a bronze. "After CWG this is my first global event and I wanted to win gold here", the Assam girl said. But despite that Mary Kom won the game and proceeded to the finals of the AIBA Women's World Championships 2018.
At least 25 killed as bus plunges into canal in Karnataka
Police had a hard time controlling the crowd as people living nearby thronged the accident site. 'Twenty five people have died. Thoughts and prayers with the bereaved families and with the injured. "Deeply pained the bus accident in Karnataka's Mandya ".
How to watch River Plate vs
The South American Football Federation (CONMEBOL) initially delayed the kick-off twice, before deciding to postpone. Police made arrests in the area, but it was not clear whether those were connected to the incidents.
"We understand the sensitivity of the current situation and would like to underline our solidarity with the Kingdom of Spain on this matter", Juncker and Tusk stated.
He said he had received the written guarantees he needed over Spain's role in the future of the British territory. Prosperity in the area, he said, "is a state matter". "We will remain allies, partners and friends".
Although several countries have expressed their sympathies for the Spanish case, at the same time, both the Commission and the other counties pointed that there was not much room for changes in the text.
The Daily Telegraph reported that the next stage of Mrs May's Brexit sales pitch will be on the immigration concerns believed to have been a key factor in the Leave vote.
He told the BBC: "We are asking for an article that is put on the table to be included in the Political Declaration on the future relations".
She said that the draft agreement raises constitutional questions and instead insisted on "an outcome that does not leave Northern Ireland open to the perils of increased divergence away from the rest of the United Kingdom".
The deal is expected to be signed off by the European Union member states on Sunday. Decisions at the European Council are traditionally taken by unanimity.
However, as May arrived in Brussels, multiple European Union leaders warned that they bloc would not be prepared to renegotiate the deal. But they also heard strong words from Spanish ministers that left them unwilling to call Sanchez's bluff without further talks.
THERESA MAY was put on the spot in BBC phone-in by a caller who demanded to know "without any political waffle or a convoluted answer" whether she believed her Brexit deal would be better for the United Kingdom than remaining in the EU.