"The EU27 has agreed that it will accept the UK's request for a #Brexit flextension until 31 January 2020. The decision is expected to be formalised through a written procedure," Tusk said in a tweet.
"Flextension" means flexible extension. If MPs approve the Brexit deal sooner, the UK could leave the EU before January 31, 2020.
The draft text of an agreement for the 27 EU ambassadors - seen by the BBC - includes two other possible dates for Brexit: November 30 and December 31.
It also includes a commitment that the Withdrawal Agreement on the UK's exit from the EU cannot be renegotiated in future.
The UK was due to leave the EU on Thursday, but Prime Minister Boris Johnson was required to request an extension from the bloc after Parliament, in a historic session on October 19, voted against his Brexit deal.
Johnson had repeatedly said the UK would leave on October 31 deadline "do or die", but the law - known as the Benn act - also requires him to accept the offer.
The development comes as UK MPs prepare to vote on Monday on proposals by Johnson for an early general election on December 12.
The Scottish Nationalist Party (SNP) and Liberal Democrats have also proposed an election on December 9.
Johnson said that if the vote was approved, his Brexit bill would resume its progress through Parliament until that is dissolved on November 6, the BBC reported.
Two-thirds of MPs - 434 - would have to back the motion for it to pass under the law which sets election timings.
A Downing Street source said on Sunday that MPs would vote on an election "so we can get a new Parliament".
If the vote was lost, the sources said that the government would then "look at all options" including ideas similar to those proposed by other parties.
MPs have already twice rejected a call from the Prime Minister to hold a general election.
( With inputs from IANS )