European Union leaders have granted the UK a six-month extension to Brexit, after late-night talks in Brussels.
The new deadline - 31 October - averts the prospect of the UK having to leave the EU without a deal on Friday, as MPs are still deadlocked over a deal.
European Council President Donald Tusk said his "message to British friends" was "please do not waste this time".
Theresa May, who had wanted a shorter delay, said the UK would still aim to leave the EU as soon as possible.
The UK must now hold European elections in May, or leave on 1 June without a deal.
The prime minister will later make a statement on the Brussels summit to the House of Commons, while talks with the Labour Party, aimed at reaching consensus on how to handle Brexit, are set to continue.
Mrs May tweeted: "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."
So far, MPs have rejected the withdrawal agreement Mrs May reached with other European leaders last year and they have voted against leaving the EU without a deal.
The EU has ruled out any renegotiation of the withdrawal agreement.
Before the summit, Mrs May had told leaders she wanted to move the UK's exit date from this Friday to 30 June, with the option of leaving earlier if Parliament ratified her agreement.
What is the reaction in the UK?
For Labour, shadow Brexit secretary Sir Keir Starmer called the delay to 31 October "a good thing", saying businesses would be "relieved".
He added: "Negotiations are in good faith. We all feel a deep sense of duty to break the impasse.
"But there's also this question of how on Earth do we ensure that anything this prime minister promises is actually delivered in the future because of course she's already said she's going to step down, probably within months."
One government minister told BBC political editor Laura Kuenssberg the latest delay to Brexit could mean a Conservative Party leadership contest after Easter, with a new prime minister potentially in place by June.
Former Brexit Secretary David Davis said: "There's been no progress whatsoever, really."
He added that it was still "difficult to see how" Mrs May could get her deal with the EU through Parliament and said: "The pressure on her to go will increase dramatically now, I suspect."
Scotland's First Minister Nicola Sturgeon tweeted her "relief" that the UK wouldn't be "crashing out" on Friday, adding that "allowing people to decide if they still want to leave is now imperative".
What was agreed?
- A Brexit extension "only as long as necessary" and "no longer than 31 October" to allow for the ratification of the withdrawal agreement
- The UK "must hold the elections to the European Parliament" and if it fails to do this, the UK will leave on 1 June
- The European Council reiterates there can be no reopening of the withdrawal agreement negotiations
What was the EU's message?
Donald Tusk emerged from the talks - and a subsequent meeting with Mrs May - to address reporters at a news conference at 02:15 local time (01:15 BST).
"The course of action will be entirely in the UK's hands," he said. "They can still ratify the withdrawal agreement, in which case the extension can be terminated."
Mr Tusk said the UK could also rethink its strategy or choose to "cancel Brexit altogether".
He 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. Please do not waste this time."
European Commission President Jean-Claude Juncker said: "There will probably be a European election in the UK - that might seem a bit odd, but rules are rules and we must respect European law and then we will see what happens."What did Theresa May say?
Mrs May spoke at 02:45 local time (01:45 BST). She said that, although the delay extends until 31 October, the UK can leave before then if MPs pass her withdrawal deal.
"I know that there is huge frustration from many people that I had to request this extension," she said. "The UK should have left the EU by now and I sincerely regret the fact that I have not yet been able to persuade Parliament to approve a deal."
She added: "I do not pretend the next few weeks will be easy, or there is a simple way to break the deadlock in Parliament. But we have a duty as politicians to find a way to fulfil the democratic decision of the referendum, deliver Brexit and move our country forward. Nothing is more pressing or more vital."
The PM said the UK would "continue to hold full membership rights and obligations [of the EU]" during the delay.