The low-key resignation saw Mrs May write to the joint acting chairmen of the backbench Conservative 1922 Committee, Charles Walker and Dame Cheryl Gillan, confirming the announcement she made a fortnight ago in Downing Street.
She will remain Prime Minister until Tory MPs and members complete the process of choosing her successor in late July.
Mrs May spent her last day as Tory leader in her Maidenhead constituency, with the Peterborough by-election defeat a stark illustration of the difficulties she has faced and which will now trouble her successor.
Foreign Secretary Jeremy Hunt, one of the 11 declared candidates in the race to replace her, warned there would be “no future” for the party unless Brexit is resolved.
Boris Johnson, the bookmakers’ favourite to replace Mrs May, has said that unless the UK’s withdrawal from the European Union is completed by October 31, an election would see Labour leader Jeremy Corbyn in Downing Street.
Environment Secretary Michael Gove, another leading contender, said the Peterborough result was a message that “we’ve got to come back together as a party and work together to get Brexit done”.
The Peterborough election saw the Tories slump to third place, behind victors Labour and the Brexit Party, in a seat which had traditionally been a Conservative-Labour marginal.
Esther McVey, who has promised as leader she would “embrace” a no-deal Brexit, said: “The result in Peterborough is the shape of things to come if we don’t deliver a clean Brexit on October 31.
“Our persistent thwarting of the referendum result shows that a Brexit Party vote will let Jeremy Corbyn into No 10 by the back door.”
The nominations process for the new leader will be completed on Monday, with candidates requiring the support of eight MPs to enter the race.
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 members.
Mrs May is stepping down amid a growing row with Chancellor Philip Hammond over her plans to leave with a series of big spending announcements, including a mult-ibillion-pound overhaul of England’s schools and colleges, according to the Financial Times.
Number 10 said the Prime Minister and Chancellor “meet regularly to discuss spending priorities”.
During her final weeks in office, Mrs May “will be focused on delivering and building on the domestic agenda that she has put at the heart of her premiership since she became Prime Minister”, a Number 10 spokeswoman said.
Meanwhile the leadership contenders were setting out their own policy platforms.
Health Secretary Matt Hancock set out proposals to abolish business rates for small high street firms and boost the living wage to £10.21 by 2022.
Home Secretary Sajid Javid promised to tear up major parts of the immigration policy he inherits from the Prime Minister.
He has committed to two-year post-study work visas for foreign students when they graduate, up from the existing six months. And he said it was “nonsense” to have a net migration target “that you know you can never meet”.
Andrea Leadsom promised “decisive and compassionate” leadership in her first campaign video and insisted she had the eight MP backers necessary to enter the race. Allies of Dominic Raab turned on Mr Johnson, pointing to a YouGov poll that suggested 53 per cent of people believed the former foreign secretary would make a bad prime minister - although 26 per cent said he would make a good premier.
Raab-supporting minister Nadhim Zahawi, who founded YouGov, said: “Polls show that the public is clear what they don’t want: a controversial face from the past. 53 per cent of voters think Boris Johnson would be a bad prime minister.
“This is a serious moment in our history - colleagues should follow the evidence and elect a fresh face with a serious plan capable of delivering Brexit.”
Rory Stewart pointed to the same polling, suggesting it showed him doing well - once the 60 per cent of people who did not know enough about him to have an opinion were discounted.
“I am now ahead of Boris and the other candidates,” Mr Stewart said. “This is vital as we build awareness.”
Meanwhile Conservative chairman Brandon Lewis has admitted that the party is going through a “difficult process” as two Tory MPs, including one Cabinet minister, are under pressure from local members to not stand for re-election.
Justice Secretary David Gauke and former attorney general Dominic Greive have both been asked to attend meetings of their local Conservative Associations.
Mr Greive was to attend a special meeting of his association last night after losing a vote of no confidence held by his local party in Beaconsfield earlier this year.
Mr Gauke faces a similar confidence motion on June 28 by the South West Hertfordshire Conservative Association.
After it was reported one constituent had joined the party to “have an influence over how Mr Gauke behaves,” he replied on Twitter: “He won’t.”