The Labour leader made the long-expected announcement, saying: “We have been unable to bridge important policy gaps between us.”
Without Labour support, the bill is heading for a crushing rejection by 100-plus MPs in the first week of June – paving the way for Ms May to announce her resignation.
However, the prime minister could yet make an attempt to break the impasse by staging further “indicative votes” in the Commons, in a final bid to reach a compromise.
But Labour insisted it had not signed up the plan – which laid bare the failure to reach agreement on the crucial issue of a customs union.
The talks had been expected to break down since the start of the week, as pressure grew on both sides to accept – after six weeks of trying – that an agreement was impossible.
“I am writing to let you know that I believe the talks between us about finding a compromise agreement on leaving the European Union have now gone as far as they can,” he said.
“It has become clear that, while there are some areas where compromise has been possible, we have been unable to bridge important policy gaps between us.
“Even more crucially, the increasing weakness and instability of your government means there cannot be confidence in securing whatever might be agreed between us.”
“Without significant changes, we will continue to oppose the government’s deal as we do not believe it safeguards jobs, living standards and manufacturing industry in Britain.”
The prime minister's spokesman confirmed the talks were over, saying: “It was clear to the government last night that the talks were not going to reach a conclusion.”
“We have made real progress on some issues such as workers' rights and environmental protections, but it is clear that we are not going to be able to reach a complete agreement.
“In particular, there have been very challenging discussions in respect of the different positions of the two sides on customs and the holding of a second referendum.”
The spokesman said Ms May “continues to believe it is the duty of elected politicians to deliver on the result of the referendum”.
“She continues to work hard on securing the passage of the withdrawal agreement bill, so that the UK can leave the EU with a deal as soon as possible,” he added.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies