In a speech made outside Downing Street on the morning of the referendum results, Mr Cameron said: "I do not think it would be right for me to be the captain that steers our country to its next destination."
He added: "I love this country and I feel honoured to have served it and I will do everything I can in future to help this great country succeed."
Uxbridge and South Ruislip MP and former London Mayor Boris was booed by crowds gathered outside his north London home on Friday morning as he left to make a speech in which he expressed his sadness about Mr Cameron's resignation, but thanked voters for backing Brexit.
Boris was critiqued during the referendum campaign for "pushing for his own ambitions to become Prime Minister".
However, if that was indeed his intention, the arrival of a Brexit decision has paid off spectacularly as within hours the announcement that Number 10 Downing Street would be vacated had been made.
Experts have suggested someone involved with the Leave campaign is surely likely to be in prime position to take over as PM.
Paddy Power announced fresh odds this morning for Boris at 4/5, favoured over other Conservative party members.
Other names have also been mentioned for the position, such as Theresa May, Michael Gove and George Osborne.
Watch David Cameron's resignation speech in full
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