After a tetchy debate, peers voted by an overwhelming majority for the proposal forcing Ms May to seek Parliament’s backing for any withdrawal deal she agrees with the EU.
The change would also mean Ms May must win a future vote in Parliament if she decides to see through her threat of potentially pulling Britain out of the EU with no deal at all.
But the proposal was met with angry attacks from Brexiteers, with one accusing other lords of seeking to tie the Prime Minister down “by her hair, by her arms, by her legs”.
Labour, Liberal Democrat and crossbench lords joined forces with Tory rebels to push through what has come to be called the “meaningful vote” amendment to the Article 50 Bill, by 366 to 268 votes.
It is the second defeat the Lords has inflicted on Ms May over the Brexit bill, giving her the power to trigger Article 50 talks, after she and her ministers demanded it be passed by Lords unamended.
The Labour-led amendment tabled with Lib Dem and crossbench support, was backed by Tory grandee Lord Heseltine who said the UK is facing “the most momentous peacetime decision of our time”.
He added: “This amendment secures in law the Government's commitment ... to ensure that Parliament is the ultimate custodian of our national sovereignty.
“It ensures that Parliament has the critical role in determining the future that we will bequeath to generations of young people.”
Up to now Ms May has only given a verbal assurance that Parliament will have a vote on the terms that she agrees and has said that if MPs and peers reject it, then the UK would still leave the EU with no deal in place.
She also made clear in her Brexit speech at Lancaster House that if she is not offered favourable terms by European leaders she will not be afraid to leave with no deal.
Proposing the amendment Labour’s Baroness Hayter said the chamber had heard a “compelling case for a simple demand”.
She added: “The Prime Minister has said she will allow a vote in both Houses ... but that to me is not a very firm commitment no matter how sincerely it was given.”
The amendment was also supported by Lord Pannick who worked on the Supreme Court case which forced the Government to let Parliament vote on triggering Article 50.
Addressing fellow peers, the crossbencher said: “It must be for Parliament to decide whether to prefer no deal or the deal offered by the EU.”
Lord Pannick added that the amendment would not delay notification of withdrawal or commit the Government to adopt any specific approach in the negotiations.
But Tory peer Lord Forsyth accused Lord Pannick of a “clever lawyer's confection” and said the proposal was a “wrecking amendment”.
Lord Forsyth said: "This House is absolutely full of people who still haven't come to terms with the results of the referendum, and this is a clever lawyer's confection in order to reverse the results of the referendum."
He went on: “These amendments are trying to tie down the Prime Minister. Tie her down by her hair, by her arms, by her legs, in every conceivable way in order to prevent her getting an agreement, and in order to prevent us leaving the European Union.”
Following the vote Dick Newby, Leader of the Liberal Democrats in the House of Lords, said: “The Government must be held accountable as Theresa May drives the country towards a reckless hard Brexit.
“Theresa May has been offered a chance to think again, a chance to support parliamentary democracy on the biggest issue of the day.”
Brexit Secretary David Davis vowed to reverse the change when the Bill returns to the Commons.
He said: “It is clear that some in the Lords would seek to frustrate that process, and it is the Government's intention to ensure that does not happen.
“We will now aim to overturn these amendments in the House of Commons.”