It came amid bitter divisions within the Tories and open rebellion against her leadership as PM.
Boris has been seen as biding his time, and has now broken cover amid expectations he will be the favourite candidate.
He tweeted: “A very dignified statement from Theresa May. Thank you for your stoical service to our country and the Conservative Party.
"It is now time to follow her urgings: to come together and deliver Brexit."
He later said that "of course I am going to stand as Prime Minister" adding "you'l hear more" from him in the next few days.
KNOCK, KNOCK: Boris Johnson could be about to enter Downing Street as PM (Pic: GETTY)
High street bookies Ladbrokes has said Boris was the immediate favourite to replace Mrs May, at odds of 5-4.
Dominic Raab was second at 5-1, according to the company, while Andrea Leadsom and Michael Gove were tied in third place at 10-1.
They were followed by Jeremy Hunt (12-1), Penny Mordaunt, Sajid Javid and Rory Stewart (all 20-1).
May will step aside as Tory leader on June 7, and remain as Prime Minister until a new leader has been chosen.
IT ALL ENDS IN TEARS: Theresa May wept as she resigned as Prime Minister (Pic: SWNS)
Boris– who failed to become leader in 2016 – told an event in Manchester this month: “Of course Im going to go for it.”
He has long been seen as the frontrunner with big support amongst the grassroots Tory.
In a documentary in 2013, BoJo said being Prime Minister "would be a great, great thing to have a crack at", if "the ball came loose from the back of the scrum".
After resigning from his post at foreign secretary he has been critical of May, and now sits with the bookies at 5/2.
STARTING GUN: Boris Johnson had already declared his intention to run for PM (Pic: GETTY) Related Articles
BOOKIES: Boris Johnson has been tipped for the top job (Pic: GETTY)
May was driven out of Downing Street by the rear exit accompanied by her husband Philip and escorted by a convoy of unmarked police cars.
The Prime Minister said she had "done my best" to get her Withdrawal Agreement through Parliament and take the UK out of the European Union.
Watched by husband Philip and her closest aides, an emotional Mrs May said it was in the "best intRead More – Source