Cameron, 48, said if re-elected in the May 7 general election he would serve the full five years of his second term in Parliament and then leave 10 Downing Street.
After that, he said, "It will be time for new leadership".
The Conservative party chief tipped UK Home Secretary Theresa May, Chancellor George Osborne and London Mayor Boris Johnson as potential successors.
"There definitely comes a time where a fresh pair of eyes and fresh leadership would be good, and the Conservative Party has got some great people coming up -- the Theresa Mays, and the George Osbornes, and the Boris Johnsons. You know, there's plenty of talent there. I'm surrounded by very good people," he told the BBC.
"I've said I'll stand for a full second term, but I think after that it will be time for new leadership." It is likely to spark intense speculation about who will succeed Cameron, an issue which is likely to dominate the next Parliament if the Conservatives win.
"I am putting myself forward for the full five years. I feel fit enough and healthy enough to do the job. I've got a real passion for it and I'm really keen to win. If I fall short I'll be disappointed," Cameron added.
"I'm standing for a full second term. I'm not saying all prime minister's all necessarily definitely go mad, or even go mad at the same rate, but I think I've got more to bring in this job. The economy has turned round, the deficit is down, I want to finish the job," he said.
Cameron was elected Conservative Party leader in 2005, and became British prime minister in 2010 at the head of the coalition government with the Liberal Democrats. He revealed his intentions in a wide-ranging interview in the latest of a BBC series looking behind the politics of the party leaders.
The Opposition Labour said Cameron was ‘taking the British public for granted’.
Shadow Foreign Secretary Douglas Alexander, the party's general election co-ordinator, said: "It is typically arrogant of David Cameron to presume a third Tory term in 2020 before the British public have been given the chance to have their say in this election.
"In the UK it is for the British people and not the prime minister to decide who stays in power."