Johnson's move came after lawmakers backed a proposal to withhold approval for his deal until formal ratification legislation has passed.
Tusk confirmed he has received the extension request from Johnson.
"The extension request has just arrived. I will now start consulting EU leaders on how to react," Tusk wrote on Twitter.
The British MPs earlier in the day voted to delay the decision on the UK's exit from the European Union (EU), ruling out a no-deal Brexit on October 31.
MP Oliver Letwin, who proposed the plan, said that his amendment was an "insurance policy" to ensure that the UK would not "crash out" of the EU without an agreement on October 31. It was passed by 322 votes to 306, CNN reported.
The decision to delay the Brexit vote comes as a fresh setback for Johnson, who will now be forced to seek an extension to Brexit.
"Alas, the opportunity to have a meaningful vote has effectively been passed up," Johnson said in Parliament, after losing the vote.
"The best thing for the UK and for the whole of Europe is for us to leave with this new deal on October 31," added Johnson.
This comes after the UK and the EU struck a new deal on Thursday after days of intense back-and-forth negotiations, setting the stage for another major parliamentary showdown over the UK's bid to leave the bloc after months of political chaos.
The UK's House of Commons has previously rejected the deal on three occasions.
The new Brexit deal comes with less than two weeks remaining for the UK to exit the EU.
The ruling Conservative Party has been struggling to finalise a Brexit agreement which has faced opposition and rejection by British lawmakers in the Parliament for the past several months.
Since taking office in July, Johnson has vowed to take his country out of the EU on October 31, with or without a deal.