Many pro-EU lawmakers want Parliament to be able to send the government back to the negotiating table if they don't like the terms of the deal, or if talks with the bloc break down.
Her concession to discuss the changes may mean lawmakers could have more power if she fails to secure a Brexit deal, possibly leading to a softer approach to Britain's divorce.
But Britain - and its government - remain divided over Brexit, and European Union leaders are frustrated with what they see as a lack of firm proposals from the U.K about future relations.
Liberal Democrat Brexit spokesman Tom Brake said: "As has become a tradition in Brexit negotiations, the Tories have been forced to cobble together a compromise".
The government said it would produce its revised plan on Thursday.
He said a concession of this kind would been "revolutionary" as the Commons can not override the government when it came to negotiating global treaties.
The government was braced for a tight battle after junior justice minister Phillip Lee, a personal friend of May's, resigned on Tuesday morning in order to back the veto amendment. They should find an agreement by the end of the week before the bill returns to the House of Lords. "But if we face the prospect of a "meaningless process" rather than a "meaningful vote", Parliament will be enraged". Just hours earlier, Downing Street had signalled the prime minister had no intention of accepting Grieve's compromise amendment to the European Union withdrawal bill, tabled by the former attorney general and aimed at ensuring ministers can't "crash out of the European Union by ministerial fiat", as he called it.
The Labour Party's Chuka Umunna, who backed staying in the European Union, welcomed the concession as the end of the government threatening to allow Britain to crash out of the European Union without a deal.
He later claimed Mr Johnson "inhabited a parallel universe" in which the referendum result is not respected "unless you want friction at the borders and disruption of the economy".
However, her concession to "seek to negotiate" a "customs arrangement" with the European Union was enough to placate Conservative MPs who were threatening to rebel.
"That is why I will be voting for my frontbench's amendment but also the Lords' amendment too".
He said his main objection to government policy was over the "wish to limit Parliament's role in contributing to the final outcome" - the so-called meaningful vote amendment.
But, the pro-EU MPs' version of what they were promised appears to differ from what they government says it offered, threatening to reignite the dispute and reviving the possibility of a revolt that would badly damage May's authority. But it's also worth recalling that the wording of his amendment was later deemed so weak that the Lords had to beef it up.
So the rebels might sit tight until July, when they will have another opportunity to force May to change direction and keep closer ties to the bloc.
May said the government would amend the bill to address legislators' concerns, but warned that "I can not countenance Parliament being able to overturn the will of the British people". "It is the Labour Party that is trying to stop us getting a deal for the British people".