Theresa May has agreed to the EU's offer of a "flexible extension" to Article 50 until October 31, with a review on progress in June, giving her six more months to either ratify or rethink her withdrawal deal.
The second extension to the Brexit process - initially intended to conclude on March 29 - definitively stopped the clock on a no-deal withdrawal on Friday with less than 48 hours to go.
In an early-hours press conference, European Council President Donald Tusk did not rule out further extensions beyond October.
He ended by saying that during the extension period the "course of action will be entirely in the UK's hands", warning the UK "please do not waste this time".
Mrs May will face MPs on Thursday when she makes a statement to the House of Commons.
However she is expected to be met with frustration from Tory Eurosceptics who will question whether she can continue to stay in power.
Leading Brexiteer Jacob Rees-Mogg criticised the latest delay and said there was "some symbolism" in the new Halloween Brexit date.
Addressing the press shortly before 2am (at almost 3am local time), Mrs May said that she still wanted the UK to leave the EU "as soon as possible".
While Mr Tusk had appeared to suggest another extension later this year could be possible, the Prime Minister insisted that Article 50 had been extended until "the end of October at the latest".
If a withdrawal deal could be ratified within the first three weeks of May, the UK could still avoid participation in that month's European Parliament elections and leave the EU in June, she said.
Acknowledging "huge frustration" among voters that the UK has not yet left the EU, she said: "The choices we now face are stark and the timetable is clear.
"So we must now press on at pace with our efforts to reach a consensus on a deal that is in the national interest."
DUP leader Arlene Foster, former Tory leader Iain Duncan Smith, Cabinet minister Owen Paterson and MEP for the DUP party Diane Dodds were meeting EU chief negotiator Michel Barnier on Thursday to discuss issues related to the Northern Ireland backstop.
Speaking after the talks, Mrs Foster said: "We wanted to have the unionist voice heard so that he could hear the impact of the backstop and what it will do to the balance in Northern Ireland.
"We had good engagement around that issue today."
Asked if she still had confidence in Theresa May, Mrs Foster said: "As you know the confidence and supply agreement that we signed was with the Conservative Party and whoever the leader of the party is we will work with.
"We believe in national stability. We want to see Brexit delivered."
Talks between the Government and Labour to find a compromise way forward will continue at official level on Thursday, Mrs May said.
"I do not pretend the next few weeks will be easy or that there is a simple way to break the deadlock in Parliament," the Prime Minister continued.
"But we have a duty as politicians to find a way to fulfill the democratic decision of the referendum, deliver Brexit and move our country forward. Nothing is more pressing or more vital."
Mrs May added that the choices the UK faces "are stark and the timetable is clear", and urged parliamentarians to "press on with pace in our efforts to reach a consensus".
The Prime Minister added that during the extra six-months in the EU, "the UK will continue to hold full membership rights, as well as its obligations."
- Watch Theresa May's press conference in full
Speaking at a separate press conference, Mr Tusk said that the Withdrawal Agreement cannot be reopened and changed, but the UK can revoke Article 50 should it choose.
The European Council President added: "Let me finish with a message to our British friends: This extension is as flexible as I expected, and a little bit shorter than I expected, but it's still enough to find the best possible solution".
Speaking alongside Mr Tusk, European Commission President Jean-Claude Juncker said that no-deal would be a "disaster".
He added that a review of progress on Brexit will take place in June and will involve the EU "taking stock", adding that it is "not another cliff edge".
The six-month extension was a compromise solution thrashed out in five hours of talks in Mrs May's absence, after French President Emmanuel Macron held out against a longer extension lasting into 2020.
Under the terms of the agreement, the UK can leave at any time if the Withdrawal Agreement reached last November is ratified by the Westminster Parliament.
If the UK fails to take part in elections to the European Parliament on May 23-26, it will automatically leave without a deal on June 1.
A review of progress will take place at the scheduled June 20 European Council summit in Brussels, but Mr Tusk stressed that this would be an opportunity for "taking stock" and not for any new negotiations.
The term of the current European Commission under Mr Juncker ends on October 31.
A UK exit by that date would get round the diplomatically awkward requirement for London to appoint a new Commissioner to his successor's team.
- What have MPs in the UK said?
Commons Leader and prominent Leave backer Andrea Leadsom played down speculation the latest delay could mean the end of Brexit.
She said "we have to use the time to deliver the Brexit we are all looking for."
Labour leader Jeremy Corbyn welcomed comments from Irish Taoiseach Leo Varadkar suggesting he is ready to contemplate a role for the UK in helping decide EU trade policies if it remains in a customs union after Brexit.
Mr Varadkar said it would be in the UK's interests to remain within the European trading bloc.
And he added: "It's also in our interest to have the UK to be in our bloc and I think we would be generous in understanding that the UK couldn't be a silent partner and would have to have a say in decisions being made."
A customs union arrangement with a British say on trade deals is a central plank of Labour's plan for Brexit.
Mr Corbyn responded with a tweet: "The Irish prime minister Leo Varadkar has confirmed this evening that Labour's alternative plan for a new customs union with a UK say on future trade deals is credible and deliverable."
While Labour MP Mary Creagh called the extension "sensible".
Other MPs reacted with outrage at the Brexit delay.
Labour MP Neil Coyle launched a scathing attack of the extension on Twitter, saying it had been achieved by a "a living dead Government run by a Party funded by the deceased".
Chuka Umunna, spokesperson for The Independent Group of breakaway MPs, said the extension provided an opportunity for a second referendum.
Citing Mr Muscat's tweet, he said: "Unless the main party leaders do a backroom deal to enable a customs union Brexit and deny the British people a say over this mess - a big risk - this extension paves the way" for European elections and a second referendum "which we must grab with two hands for the sake of future generations.
"With British MEPs continuing to sit in the Euro Parliament we will be rule makers not rule takers - if Brexit had happened and the UK was in transition, it would have been the opposite.
" A #PeoplesVote with Remain on the ballot will give voters a chance to make this permanent."
- What have EU leaders said about the extension?
Malta's Prime Minister, Joseph Muscat, tweeted that the extension was "sensible" as it would give the UK "time" to "finally choose its way", adding that a "review in June" will allow the EU 27 to "take stock of the situation".
Polish Prime Minister Mateusz Morawiecki said the delay gives time to overcome the "crisis" in the Commons.
"We moved away the risk of no-deal Brexit for a several months," he tweeted.
"It gives a chance to overcome the ratification crisis in UK. It is now up to UK to take this opportunity."