Chairman of the Conservative backbench 1922 Committee Sir Graham Brady announced the vote this morning – with it due to be held tonight between 6pm and 8pm.
Mrs May said she will contest the leadership challenge – and said it will be damaging to Britain to change leadership now.
And her Cabinet ministers have rallied around the PM as the Tory party looks set for a brutal battle – with warnings it could delay Brexit.
Sir Graham said he told the Prime Minister the threshold had been met last night, and that she wanted the matter to be resolved as rapidly as reasonably possible.
Mrs May has been desperately trying to smooth over the divisions in her party as she attempts to push through her Brexit deal.
“In the national interest, she must go”
Jacob Rees-Mogg and Steve Baker
The Prime Minister pulled the "meaningful vote" on the deal from the House of Commons, much to the fury of MPs, and has since embarked on a whistle-stop tour around Europe.
She is looking to secure clarification on her deal – the Brexit Withdrawal Agreement – before bringing it back to the House of Commons.
Mrs May visited The Hague, Berlin and Brussels yesterday as she attempted to drum up support on the continent – with Brexit just 107 days away on March 29.
Meanwhile, plotters were scheming back at home – finally reaching the key number of 48 letters needed to trigger a vote of no-confidence in PM.
NO-CONFIDENCE: Theresa May faces a major challenge to her future as PM (Pic: EPA)
Justice Secretary David Gauke said that if Theresa May loses a vote of no confidence "the first thing the next Prime Minister will have to do is delay Brexit”.
Earlier, unconfirmed reports suggested Sir Graham had asked to meet Mrs May after Prime Minister's Questions on Wednesday afternoon.
Former cabinet minister Owen Paterson was the latest MP to declare he had submitted a letter to the chairman of the backbench 1922 Committee.
Speculation that a challenge could be imminent was fuelled after chief whip Julian Smith and Conservative Party chairman Brandon Lewis were seen leaving No 10 following late-night consultations on Tuesday.
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In a joint statement the chairman of the European Research Group Jacob Rees-Mogg and his deputy Steve Baker said: "Theresa May's plan would bring down the Government if carried forward. But our party will rightly not tolerate it.
"Conservatives must now answer whether they wish to draw ever closer to an election under Mrs May's leadership. In the national interest, she must go.”
Rees-Mogg fired the starting gun on the coup last month when he stood on the steps of Westminster and called for his colleague to unseat Mrs May.
The number of letters has slowly been creeping up since then, and has been pushed over the edge by the PMs latest backtrack over the “meaningful vote”.
CONFIRMED: Sir Graham Brady issued the statement confirming the vote (Pic: PA)
Foreign secretary Jeremy Hunt said: "I am backing Theresa May tonight. Being PM most difficult job imaginable right now and the last thing the country needs is a damaging and long leadership contest.
"Brexit was never going to be easy but she is the best person to make sure we actually leave the EU on March 29."
Pensions Secretary Amber Rudd, who recently returned to the Government, tweeted: "The PM has my full support. At this critical time we need to support and work with the PM to deliver on leaving the EU, & our domestic agenda – ambitious for improvements to people's lives & to build on growth of wages and jobs.”
Home Secretary Sajid Javid said: "The last thing our country needs right now is a Conservative Party leadership election. Will be seen as self-indulgent and wrong.
"PM has my full support and is best person to ensure we leave EU on 29 March."
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Chancellor Philip Hammond was another Cabinet minister to come out in support of Mrs May, tweeting: "The Prime Minister has worked hard in the national interest since the day she took office and will have my full support in the vote tonight.
"Her deal means we leave the EU on time, whist protecting our jobs and our businesses."
Communities Secretary James Brokenshire also tweeted: "Strongly support @theresa_may to continue as Leader of @Conservatives and Prime Minister.
"Now is not the time for this distraction and even more uncertainty. We need to get behind the Prime Minister in the best interests of our country."
REMAIN: Britain is leaving the EU on March 29 (Pic: GETTY)
Environment Secretary Michael Gove, another Cabinet minister who had been touted as a possible leadership contender, tweeted: "I am backing the Prime Minister 100% – and I urge every Conservative MP to do the same.
"She is battling hard for our country and no one is better placed to ensure we deliver on the British people's decision to leave the EU."
Education Secretary Damian Hinds tweeted: "Let's all get behind Theresa May to complete the job on brexit and keep on delivering on jobs & growth and tackling injustices. A leadership challenge does nothing to secure Brexit, andis the last thing our country, or the party, needs at this critical time."
Transport Secretary and prominent Brexiteer Chris Grayling said: "I will be backing Theresa May tonight. At this crucial point, the last thing the country needs is a prolonged and introspective leadership contest.
"I was one of the first Cabinet ministers to back Brexit. Delivering a deal was never going to be simple.
"Theresa May is the best person to make sure we actually leave the EU and deliver on the Brexit that I and the people of our great country voted for."
PEOPLE'S VOTE: Campaigners descend on Westminster amid Brexit chaos (Pic: REUTERS)
Liberal Democrats leader Sir Vince Cable tweeted: "The self-indulgent ToryParty leadership challenge is about more than choice of leader.
"Political logic demands a split into a @UKIP style populist anti-EU party and another of the sensible centrists working with others. Stop Brexit chaos. People's vote now."
International Trade Secretary Dr Liam Fox tweeted: "I will support the Prime Minister Theresa May tonight. This is a totally inappropriate time to have a contest.
"The country expects us to provide stability not damaging division."
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The chairman of the backbench 1922 committee of Conservative MPs said: "The threshold of 15% of the parliamentary party seeking a vote of confidence in the leader of the Conservative Party has been exceeded.
"In accordance with the rules, a ballot will be held between 1800 and 2000 on Wednesday 12th December in committee room 14 of the House of Commons.
"The votes will be counted immediately afterwards and an announcement will be made as soon as possible in the evening.
"Arrangements for the announcement will be released later today.
"I will be available to answer questions about this process on Abingdon Green from 0800 hrs."