The full result of the second-round ballot of MPs was:
David Cameron 90 (56 in first ballot)
David Davis 57 (62 in first ballot)
Liam Fox 51 (42 in first ballot)
Dr Fox joins Kenneth Clarke as a loser in the MPs' votes for the party's leadership, following the resignationation of Michael Howard.
Mr Cameron, aged 39, who gained 34 votes compared with the first round, said: "I'm looking forward to taking my message right round the country. It's going to be a lot of hard work, but I am very excited by it.
"I want to be a voice for change, for optimism and for hope in this country.
"I want us to confront the big challenges that this country faces: making sure we have a strong economy so we can generate the jobs we need; reforming public services so we can have good schools and hospitals for everybody; stronger communities; stronger families; and a good quality of life.
"I want a party that looks to the future, a party that is a 21st century party and is modern and compassionate and understands the aspirations and hopes and dreams of the people."
The vote seals Mr Cameron's position as the overwhelming favourite to succeed Michael Howard as party leader.
Mr Davis, aged 56, who lost five votes from his first-round total, said: "There's a long time to go in this contest yet, still another six weeks. I intend to fight for my beliefs.
"I'm going to start the process by going to my old University of Warwick tomorrow to carry to members of the party and others my beliefs - an opportunity society, in hope for Britain, in changing Britain to improve lives, and particularly to address the issue of reaching those parts of Britain that the Conservative Party hasn't reached for too long."
Dr Fox, aged 44, who gained nine votes over his first-round total, said: "With two candidates left they will be looking for an endorsement ... and I want to endorse the programme that I have been setting out for a few weeks."
He would be listening "with very great interest" to what the candidates would be saying.
The result sparked immediate speculation that some of Mr Cameron's supporters had voted for Mr Davis to knock out Dr Fox.
However the shadow Home Secretary's backers were swift to point out that 55 per cent of the parliamentary party had not voted for Mr Cameron.
Sir Nicholas Winterton called on Liam Fox to come out for Mr Davis and campaign on his behalf. He said: "We want to give the golden boy a good run for his money and he has had a lot of that more than the others."