Amid criticism of the deal from lawmakers on all sides of Britain's EU debate, European Commission chief Jean-Claude Juncker said the United Kingdom couldn't hope to negotiate better terms before its departure in March.
The British government wrote to Mr Tusk to say that it would not interpret its withdrawal treaty as meaning that a future EU-UK trade treaty would automatically apply to Gibraltar - but it would seek the best deal for the territory.
At a special summit in Brussels that was nearly derailed by a row over Gibraltar, the other 27 leaders will gather to sign off the agreement before May joins them to mark the milestone.
The prime minister said her agreement promises a "brighter future" for the United Kingdom and leaving the European Union next year will be "a moment of renewal and reconciliation for our whole country".
It added that the EU's approach will continue to be defined by the overall positions and principles set out in the previously agreed European Council's guidelines and the Council will remain permanently seized of the matter.
She added that the DUP would "review" their agreement to prop up May's government if the deal were passed by Parliament.
After a meeting in Brussels Friday of senior European Union officials, the Spanish government said negotiations were continuing but not enough progress had been made to drop the veto threat. I want that to be a moment of renewal and reconciliation for our whole country. In a bid to help the prime minister, he said May had "fought very hard" and now there was "an acceptable deal on the table".
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May is under intense pressure from pro-Brexit and pro-EU British lawmakers, with large numbers on both sides of the debate opposing the divorce deal and threatening to vote it down when it comes to Parliament next month.
Sunday newspapers said different factions in her own Conservative party were preparing alternative plans to keep Britain closer to the European Union should her deal fail as many expect.
European Council President Tusk said the bloc was determined to have as close as possible a partnership with Britain, which has always been sceptical about EU integration: "We will remain friends until the end of days".
The European Council also approved the Political Declaration setting out the framework for the future relationship between the EU and Britain.
"But I must tell him that whilst he pursues the sovereignty of Gibraltar in the manner that he has today, he is doing no more than pursuing the policy bidding of the Generalissimo himself". He told reporters that the summit "is neither a time of jubilation nor of celebration".
Theresa May, who met with Mr Tusk and the presidents of the European Parliament and Commission on Saturday evening, was not present but will join the summit later on Sunday morning.
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"It would not be a good idea to lecture the House", Juncker said, but insisted that it was only deal possible.
According to the Sunday Times, Chancellor Philip Hammond is working with other Cabinet ministers to try to persuade Mrs May to opt for a softer Brexit deal, which they believe could get through Parliament if her original deal is rejected.
Foreign Minister Augusto Santos Silva says that the original Brexit guidelines laid out a year ago that included assurances to Spain that it could deal with London directly on the issue of Gibraltar were "wise".
If the United Kingdom parliament approves the deal, which seems unlikely, then the British government would propose new legislation in January, which would then need to be approved by parliament before it becomes law.
"There's a danger we end up through this transition deal of losing Gibraltar and Northern Ireland", he said.
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