Fellow MP Antoinette Sandbach rejected suggestions by leading Brexiteers in her party that this would tie the prime minister's hands in negotiations.
Earlier, the Government was hit by its first resignation over Brexit strategy, as Justice Minister Phillip Lee quit.
He accused the Government of trying to "limit" Parliament's role and called for another referendum once ministers' chosen path becomes clear.
British Prime Minister Theresa May faces a knife-edge vote in parliament on June 12 on her centrepiece Brexit legislation, despite her last-minute warning that defeat risks undermining her negotiations with Brussels.
Theresa May is facing one of the biggest tests of her leadership, with Tory rebels threatening to vote against their own party to force through amendments to the bill.
Earlier this year, Lee had called on the government to release its economic impact assessments of Brexit and suggested the government change tack in talks with the European Union, underlining the deep rifts in his party over the best way to manage Britain's exit. "A meaningful vote is not the ability to reverse the decision of the referendum".
These were the words of a minister expecting to win the vote.
The concession on a meaningful vote came after intensive horse-trading on the floor of the House of Commons, with chief whip Julian Smith shuttling between Tory backbenchers during debate on Lords amendments to the EU Withdrawal Bill.More news: Kate Middleton perfected summer style in a $70 Zara dress
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The government has avoided a major defeat on its Brexit bill by 324 votes to 298 after a late concession.
If the government fails to pass the bill as it is, it will be forced to change what it asks for in negotiations with the European Union -undermining May's position and possibly threatening her job as Prime Minister.
However, a potential rebellion by pro-Remain Tories over their demands for a "meaningful vote" on the final Brexit deal was only avoided after ministers agreed at the last moment to discuss a compromise.
At the very least, Grieve and his colleagues have succeeded in throwing up a series of new parliamentary barriers to a no-deal Brexit.
The former attorney general said he expected two parts of his amendment to be taken on by the Government, stating: "The two parts provide the mechanism by which Parliament has to be consulted in the event of no deal and the Government come forward with a motion explaining what it will do".
The final vote, as outlined in Grieve third point, would be different as the government would then have to follow any direction given by the Commons. She now relies on the support of a small Northern Irish party.
Brexit protesters outside Parliament House.
May's government is divided between Brexit-backing ministers such as Foreign Secretary Boris Johnson who support a clean break with the European Union, and those such as Treasury chief Philip Hammond who want to keep closely aligned to the bloc, Britain's biggest trading partner.