Theresa May will take the keys to No 10 by Wednesday evening, David Cameron has confirmed.
The Prime Minister said he was "delighted" that the Home Secretary would succeed him in Downing Street and he will go to the Palace to offer his resignation to the Queen on Wednesday afternoon.
Cameron hailed his successor, who becomes the Conservative's second woman Prime Minister, as "strong and competent".
"We're not going to have a prolonged Conservative leadership election campaign," said Cameron.
"I think Andrea Leadsom has made absolutely the right decision to stand aside and it's clear Theresa May has the overwhelming support of the Conservative parliamentary party.
"I'm also delighted that Theresa May will be the next prime minister - she is strong, she is competent, she is more than able to provide the leadership that are country is going to need in the years ahead and she will have my full support.
"Obviously with these changes we now don't need to have a prolonged period of transition and so tomorrow I will chair my last Cabinet meeting, on Wednesday I will attend the House of Commons for Prime Minister's Questions, and then after that I expect to go to the Palace and offer my resignation.
"So we will have a new prime minister in that building behind me by Wednesday evening."
Cameron will chair his last Cabinet meeting tomorrow morning and appear in the Commons for the final time as premier when he takes to the Despatch Box for Prime Minister's Questions at noon on Wednesday.