The EU also wants more clarity from the United Kingdom on what sort of trade and future relationship it envisages after Brexit to be able to start discussions on that future after March, when EU leaders adopt another set of guidelines for those talks.
Talks on phase two are set to begin in January.
She said Britain would be "beginning the talks about our future relationship straight away", adding: "There is still more to do but we are well on the road to delivering a Brexit that will make Britain strong, prosperous and secure". The document leaves no doubt that a formal free trade agreement can not be signed until after the United Kingdom has left.
As May left to return to London - she will not join the other 27 leaders for further discussions on Brexit and the euro zone - she said she was eager to move on, once her peers give the formal green light to trade talks on Friday.
"I'm looking forward to discussing that deep and special partnership for the future", May said as she arrived for the summit.
Asked if a final deal by March 2019 - Britain's exit date - could be achieved, Tusk insisted it was "still realistic and of course dramatically difficult".
The EU has published its guidelines for phase two of the negotiations, with discussions on future economic co-operation not likely to begin until March.
At Friday's meeting, the leaders said Friday "sufficient progress" had been reached on the outstanding European Union bill Britain will have to pay, the rights of citizens in each other's areas and the commitment to maintain a transparent border between Ireland and Northern Ireland.
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The three-page document says the United Kingdom will remain under the jurisdiction of the European Court of Justice and be required to permit freedom of movement during any transition period.
Speaking in London after confirmation that talks will now start in the new year on Britain's future relationship with the EU, Labor's Jeremy Corbyn said: "This should have happened months ago".
Meanwhile, her hopes of avoiding a second Commons defeat over Brexit also improved after senior Tory backbenchers from both the Leave and Remain factions appeared to be ready to back a compromise over Mrs May's plan to write the date the United Kingdom leaves the European Union into law.
Senior ministers are due to have their first discussion of the "end state" relationship Britain is seeking with the European Union in a Cabinet meeting next Tuesday which threatens to expose deep divisions between their visions of the UK's future.
Paul Masterton, a potential Tory rebel who abstained in the defeat on Wednesday, said it was a "sensible amendment to the Withdrawal Bill that gives us flexibility on Brexit date if we need".
May replied on Twitter, thanking Tusk and European Commission President Jean-Claude Juncker and hailing it as a major advance in the negotiations.
Mr Juncker said he was "convinced" a legally binding withdrawal agreement will be signed by October, to allow time for ratification by the European Parliament and MPs in Westminster.