Grieve, who earlier said he woke up in the small hours worrying that his actions would bring down the PM, said after the vote: "We've managed to reach a compromise without breaking the Government - and I think some people don't realise we were getting quite close to that".
Mr Grieve had tabled an amendment to the bill, requiring MPs to be given the opportunity to approve or reject the Government's plans for the next steps in the case that no agreement can be reached with Brussels by Brexit Day in March next year. One of the leading Brexiteers, Jacob Rees-Mogg MP, said the Prime minister can now attend the European Union leaders summit next week "with full strength" now that the legislation to the leave the European Union was part of UK Law, according to the BBC.
Under the deal, an official ministerial statement will be issued on Thursday making clear it is ultimately for Speaker John Bercow to decide whether they get a "meaningful vote" on a no-deal withdrawal from the EU.
But worldwide trade secretary Liam Fox said nothing had really changed and the option of a no-deal Brexit had been left firmly on the table.
He said the government had "to be able to hold out in our negotiations the prospect of no deal" otherwise the European Union would get the upper hand.
The BBC's Laura Kuenssberg says the government should be anxious by how tight the vote was, even after the compromise was struck with Grieve, which could be a sign of "big problems ahead".
The government was anxious enough about losing today to budge, even if they only gave an inch.
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"The climbdown will be a huge relief to the Prime Minister, who had warned her whole Brexit strategy could be derailed if Mr Grieve's 'meaningful vote" amendment had been passed.
His move opened a split within the ranks of the potential rebels, who had previously numbered around 15.
Pro-EU lawmakers later accused the government of going back on its word by offering only a symbolic "take it or leave it" vote on the final deal and not the ability to take control of the negotiations.
MPs will then vote on this statement. Relationships between MPs had been "strained nearly beyond belief", she said.
In what was a nail-biting finale to several weeks of intense debates in both the House of Commons and the House of Lords, MPs by 319 votes to 303 rejected the proposal put forward by Grieve.
Mr Grieve said he had insisted on a key paragraph in the statement, saying the government "is open to MPs to table motions and debate matters of concern and that, as is the convention, parliamentary time will be provided for this". Other rebels have also reportedly, "called off the revolt", including former cabinet minister Nicky Morgan.