Theresa May has promised Tory MPs she will stand down if they back her deal.
She told backbench Tories: "I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party."
The PM said she knew that Tory MPs did not want her to lead the next phase of Brexit negotiations "and I won't stand in the way of that".
Boris Johnson has said he will now back the prime minister's deal, the BBC's Laura Kuenssberg said.
Mrs May did not name a departure date at a packed meeting of the 1922 committee.
But Laura Kuenssberg said a Tory leadership contest could be expected in May.
Downing Street said it would be a "different ball game" if the deal was not passed by Parliament.
It comes as MPs seize control of the Commons agenda to hold votes on alternatives to the deal.
Mrs May told the 300 or so Tory MPs at the meeting "we need to get the deal through and deliver Brexit".
"I ask everyone in this room to back the deal so we can complete our historic duty - to deliver on the decision of the British people and leave the European Union with a smooth and orderly exit."
Labour leader Jeremy Corbyn tweeted that Mrs May's announcement "shows once and for all that her chaotic Brexit negotiations have been about party management, not principles or the public interest".
He added: "A change of government can't be a Tory stitch-up, the people must decide."
SPEAKER CALLS FOR CHANGES
Tory MP Simon Hart said the mood in the 1922 meeting was "respectful" as the prime minister set out her plan.
He said: "She was passionate about getting the deal through, passionate about keeping the party together and passionate about keeping the government as the government, passionate about keeping Jeremy Corbyn out of Number 10."
Despite the nature of the meeting, Mr Hart joked that "neither the Chief Whip nor the PM were crying".
The PM has said she wants to bring the deal back to the Commons this week, after it was previously rejected twice, by large margins.
Commons Speaker John Bercow ruled last week that the government could not return for a third attempt, unless there had been "substantial" changes to the proposals.
And he warned ministers earlier that they should "not seek to circumvent my ruling" by introducing procedures that could reverse his judgement.
But a Downing Street spokesman said there had been a "significant development" at the summit in Brussels last week, after Mrs May agreed "extra reassurances" over the Irish backstop with the EU, and the date of exit had changed.