The government will bring forward this week the domestic legislation needed to implement the divorce deal, with a first vote as soon as Tuesday.
"EU Council President Donald Tusk tweeted that he had received the extension request and would consult EU leaders 'on how to react'".
Johnson very much wants Britain to leave the bloc on October 31 but British lawmakers have not yet voted on his new Brexit plan.
The Letwin amendment saw him send a Brexit deadline extension letter to Brussels at the weekend.
Over the weekend, UK Prime Minister Johnson's attempt to get parliamentary approval for his Brexit deal fell flat - not because of inadequate support for his bill, but because of an earlier amendment put forward by Sir Letwin, created to avoid any meaningful vote on the bill until details of implementation had been finalized.More news: Speculation over Brexit deal based on major shift by United Kingdom government
In a twist that illustrates the extent to which Brexit has strained the norms of British statecraft, Johnson sent the note to the European Union unsigned - and added another signed letter arguing against what he cast as a deeply corrosive delay.
Having cut a new deal with European Union negotiators last week, the prime minister meant to bring it to Parliament on Saturday and to ask parliamentarians to deliver a "meaningful" domestic vote. This move was aimed at preventing hardline Brexiters blocking a subsequent withdrawal bill as the clock ticks to October 31, in order to engineer the "no deal" scenario that many of them want.
Demonstrators march during the People's Vote Together for the Final Say March, in London, Britain.
"Whether it's [British prime minister] Boris Johnson's bad deal or a better one which could be secured, it has got to go to a referendum up against remain", Labour leader Jeremy Corbyn also said.
European Union officials have not responded to the request.
"The request was accompanied by a second letter, signed by Mr Johnson, saying he believes a delay would be a mistake".More news: United States bombed own airbase in Syria before withdrawing troops
"I will tell the European Union what I have told the British public for my 88 days as prime minister: further delay is not a solution", he said.
His attempt to fulfil the letter of the Letwin law but not the substance of it was called "childlike" by Labour.
Johnson could face legal challenges from opponents who feel that sending the second letter was done to frustrate Parliament, which has not approved his Brexit plan but does want to avoid a no-deal Brexit.
The Court of Session in Scotland is already considering the matter, and it may end up being decided in the British Supreme Court, which in September ruled that Johnson had acted unlawfully when he suspended Parliament for five weeks as the Brexit deadline crept closer.
Johnson has been determined to take the country out of the 28-nation bloc on October 31, but lawmakers are trying to avoid a no-deal Brexit, which economists say would wreak damage on the United Kingdom economy. For hours, British lawmakers issued both ringing endorsements and scathing condemnations of Johnson's Brexit deal, only to kick any decision on it down the road by passing an amendment withholding approval for the deal until laws enabling it are passed.More news: Rohit Sharma scores a double century, Virat Kohli and co. reacts fiercely