The prime minister had asked for a delay only until June 30, but Tusk said in a tweet that she had agreed to a longer "flexible" extension, which provides for Britain to leave any time before October 31 provided Parliament ratifies a divorce deal and passes accompanying legislation to ensure a smooth transition out of the EU.
It is long enough to mean that Britain is likely to have to take part in the European elections on May 22 - until now a clear red line for the Prime Minister.
The officials spoke to The Associated Press on condition of anonymity to discuss the closed-door negotiations.
European Council President Donald Tusk (L), Luxembourg's Prime minister Xavier Bettel (C-L), Britain's Prime minister Theresa May (C-R) Germany's Chancellor Angela Merkel (R) look at a tablet ahead of a European Council meeting on Brexit at The Europa Building at The European Parliament in Brussels on April 10, 2019.
While her bid for a 30 June deadline failed, she made clear she was not against a longer extension, as long as the United Kingdom could leave earlier.
Many leaders had wanted a much longer extension, to the end of the year or even next March, but French President Emmanuel Macron mounted stiff resistance throughout the evening, eventually forcing the compromise.
The extension to Article 50 - the mechanism that notifies when Britain will leave the European Union - does not mean negotiations will reopen between the bloc and the UK.
However, following the announcement of the extension, Mr Macintosh said a recall was no longer necessary.
Most EU leaders have signaled they could accept an extension as long as Britain promises not to use it to undermine EU policies during a transition.
May agreed a divorce deal with the European Union last November but MPs in London have rejected it three times, forcing her to turn to the main opposition Labour party in a bid to find a way through.
"What is indispensable for us is that nothing can compromise the European project in the following months", the French president said as quoted by the Washington Post.
Mrs May added: "I do not pretend the next few weeks will be easy, or there is a simple way to break the deadlock in parliament".
The poll by the Open Europe think tank ranked Labour in pole position with a considerable lead over the Conservatives, 37.8 per cent to 23 per cent, while the new Brexit Party has 10.3 per cent of voters' support. The two sides said they would resume their discussions Thursday. But they can't force her out of office until the end of the year, after she survived a no-confidence vote last December. "We have a European renaissance to implement, and I do not want the issue of Brexit to block us at this point".