Cameron said he will chair his last Cabinet meeting tomorrow and attend House of Commons for his last Prime Minister's Questions on Wednesday before heading to Buckingham Palace to offer his official resignation to Queen Elizabeth II.
"We will have a new Prime Minister in that building behind me by Wednesday evening," Cameron told reporters outside 10 Downing Street.
"I am delighted Theresa May will be Prime Minister. She has the overwhelming support of the Conservative parliamentary party...She is strong, she is competent, she is more than able to provide the leadership that our country is going to need in the years ahead," said Cameron, who had announced he would be stepping down for a new prime minister to take the Brexit negotiations forward with the European Union a day after the June 23 vote in favour of Britain leaving the economic bloc.
Earlier today, May's only rival Andrea Leadsom pulled out from the two-way contest for the Conservative party leadership in a dramatic move, leaving May sole contender.
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Leadsom, who was energy minister in the Cameron-led Cabinet, threw her support behind May as "ideally placed" to enforce the vote for Brexit in last month's referendum on Britain's membership of the European Union (EU).
"The interests of our country are best served from the immediate appointment of astrong and well-supported Prime Minister. I am therefore withdrawing from the leadership election and I wish Theresa May the very greatest success.I assure her of my full support," Leadsom told reporters.
It then fell to the 1922 committee of Conservative MPs to decide the revised timetable for the leadership race.
Conservative MPGrahamBrady, the chairman of the committee, told reporters soon after Leadsom's announcement that May is now the only candidate for the party leadership, which only leaves the formal announcement of her as party leader and PM.
Cameron's statement then confirmed that there was no need
Leadsom's withdrawal had effectively nullified the need for a postal ballot by the UK-wide Conservative party membership and made it certain that a new leader would be officially declared much sooner than the September 9 timeline initially announced.
Leadsom's announcement followed days of controversy around her candidature, which included allegations of exaggerating her curriculum vitae and most recently having to apologise to her rival over an interview to The Times which suggested that being a mother made her a better candidate for the job.
May had recently publicly revealed her own sadness at not being able to have children.
In a message to the party, he said: "Now is the time for us to unite...And get on with the job of securing a strong, prosperous future for our country."
In a speech earlier today setting out her leadership campaign platform and before the day's surprising developments, May said: "Brexit means Brexit and we're going to make a success of it."
There had originally been five contenders to succeed Cameron, with MPs voting in two rounds to get that number down to two - and the plan then was that the party's 150,000-strong membership would have had the final say.