Mrs May has confirmed her decision on Friday in an exchange of letters with the joint acting chairmen of the backbench 1922 Committee, Charles Walker and Dame Cheryl Gillan.
Under the timetable set out by the party high command, it is expected the new leader will be in place in the week beginning July 22 following a postal ballot of the party’s 120,000 grassroots members.
Mrs May leaves as party leader hours after defeat to Labour in the Peterborough by-election, where the Tories were pushed into third place by the Brexit Party.
A statement issued by the Tory backbench 1922 Committee read: "Following notification from the Prime Minister, Rt Hon Theresa May MP, that she has resigned as leader of the Conservative and Unionist Party, the joint acting chairs of the 1922 Committee are inviting nominations from those Conservative Members of Parliament who wish to stand for election as the next party leader."
Mrs May steps down amid a growing row with Chancellor Philip Hammond over her plans to leave with a series of big spending announcements – including a multi-billion pound overhaul of England’s schools and colleges – according to the Financial Times.
The reported row comes after Downing Street defended the need for ambitious action to tackle climate change following warnings from the Treasury that cutting the UK’s greenhouse gas emissions to zero by 2050 will cost £1 trillion.
Even as the formalities around Mrs May’s departure were taking place, the 11 contenders so far to declare in the race to succeed her were engaged in increasingly bitter exchanges.
Home Secretary Sajid Javid became the latest contender to denounce the idea – branding it “anti-democratic and anti-British”.
Speaking to the British Future think tank on Thursday, Mr Javid said while he wanted to leave the EU by the cut-off date of October 31, he accepted Parliament was entitled to a say.
“I wouldn’t prorogue Parliament. That is a complete nonsense. My policy would be to do everything I can to leave the European Union on October 31,” he said.
“If it got to a point where I had to choose between no deal or no Brexit, I would pick no deal. But whatever I do, Parliament is going to want have its say on it and Parliament should have its say.
“Our Parliament is sovereign. I am not into this proroguing Parliament rubbish. It is just a complete nonsense and anti-democratic and anti-British.”
Mr Javid also took a sideswipe at leadership front-runner Boris Johnson over his comments last year saying Muslim women who wear the burka looked like letter boxes.
“I think they they are wrong. I don’t think they are the right comments. I don’t think any serious politician should use language like that,” he said.