The amendment, which will be debated on Wednesday afternoon, seeks to give Parliament the power to either approve or vote down any Brexit deal reached between British and European Union negotiators before exit day in March 2019.
Tory former ministers Ken Clarke, Nicky Morgan and Anna Soubry also rebelled to support an amendment pushed by Labour's Yvette Cooper, which aimed to introduce a "necessity test" to ensure delegated powers included in the Bill should be used "only so far as necessary".
"And it is good news for people who voted Remain, who were anxious we were going to crash out without a deal".
"The written ministerial statement does not address why clause nine is needed (it is incompatible with the [written ministerial statement]) or why my amendment can not be accepted", Grieve told POLITICO.
It's in that context that the government faces a potential defeat on Wednesday on the Withdrawal Bill and must weigh up its best course of action.
Flagship Brexit legislation survived intact as it returned to the Commons despite further Tory concerns and a mini-rebellion. Tory rebels have threatened to vote against the government on a few different occasions.
And while the government today has sought to say ministers are listening, government sources say they are looking to do what they can to make peace - as things stand, it's feasible that the prime minister will be beaten in the Commons on Wednesday.
Stage set for another Brexit showdown with Tories threatening to rebel
Asked how many Tory backbenchers agreed, he replied: "I think enough, if this comes to a vote, to defeat the Government".
"And it would be really quite refreshing if you both just looked me in the eye and said 'you know what Piers, actually you are right, we are both staunch Remainers, we don't want Brexit to happen, and our real game plan here is to stop it from happening".
Conservative Eurosceptics have reacted angrily to the threatened revolt.
Former Conservative leader Iain Duncan Smith accused Mr Grieve of grandstanding and trying to tie the Government's hands in negotiations.
But Labour, which has tabled a similar amendment, signalled its backing for the change in the bill's wording.
Labour have always been clear that Parliament, not ministers, must have the final say on the UK's withdrawal agreement with the EU. If it passes both these stages, the agreement would then be brought into United Kingdom law via a new bill - the Withdrawal Agreement and Implementation Bill - which MPs would also have a vote on. Grieve urged rebels not to be bought off by "warm words and woolly concessions".
If neither ministers or unhappy Conservative MPs back down, the Government will face a crunch vote on the EU Withdrawal Bill on Wednesday night.