Julie Bishop has retained the role of deputy leader, contested by Kevin Andrews, winning with 70 votes to his 30.
It's Australia's fifth change of leader in only five years.
Stepping up for the first time as prime minister-designate, Malcolm Turnbull has paid tribute to the man he ousted four days short of two years in office.
"What a great debt the nation owes and the party owes, the Government owes, to Tony Abbott and, of course, to his family, Margie and their daughters. The burden of leadership is a very heavy one. "
Mr Turnbull's praise of Mr Abbott's achievements on free-trade agreements and border security came in sharp contrast to his earlier comments on the Prime Minister's leadership.
Announcing his intention to challenge for the role, he said Tony Abbott had failed to provide the economic leadership the nation needed.
Mr Turnbull has promised to lead what he calls a "thoroughly Liberal" Government.
"This has been a very important, sobering experience today. I'm very humbled by it. I'm very humbled by the great honour and responsibility that has been given to me today. This will be a thoroughly Liberal Government. It will be a thoroughly Liberal Government committed to freedom, the individual and the market."
Foreign Minister Julie Bishop, who did not speak publicly prior to the vote, has retained the role of deputy leader.
Defence Minister Kevin Andrews contested for the spot, but she won with 70 votes to his 30.
Ms Bishop says she is thrilled to be continuing as foreign minister.
"I came into the Liberal Party, and came into parliament, because I believed in the values of the Liberal Party. I am firmly of the view that the values and beliefs of the Liberal Party are as relevant today as they were when this great party was formed 70 years ago. In Malcolm Turnbull, we have a leader who will be true to those Menzian* values and beliefs, and I'll be honoured to serve this party and this country in my current role."
Tony Abbott did not address the media after the vote.
Speaking before the vote, he had warned his colleagues not to follow the path of the Labor Party in switching prime ministers in mid-term.
"The prime ministership of this country is not a prize or a plaything to be demanded. It should be something which is earned by a vote of the Australian people."
Opposition Leader Bill Shorten also spoke before the vote, saying a change of Liberal leaders would change nothing.
"Now Malcolm Turnbull is right that Australia has been going nowhere for the last two years with this chaotic, dysfunctional, divided Liberal Government. But Malcolm Turnbull is wrong when he says he is part of the solution. Australians know that Malcolm Turnbull is ambitious but he's ambitious for himself, not our nation. With Malcolm, it will always be about Malcolm."
It was the second formal challenge to Mr Abbott's leadership.
In February, he survived a move driven by the backbench to spill the leadership because Malcolm Turnbull did not nominate.
Mr Abbott's leadership had then been plagued by Cabinet leaks since June.
SBS chief political correspondent Catherine McGrath says it will, indeed, be difficult for the Liberal Party to move on from the leadership spill that is now a reality.
"Tony Abbott has every reason to feel very upset and very disappointed. He tried to fight through it, saying that the Liberal Party should not be like the Labor Party, overthrowing its prime minister, it shouldn't do that. And, again, he made such a point of that in the last election. So it has been a party divided. All of that is out in the public. They really have to heal those wounds, and that is not going to be straightforward."
Tony Abbott's term as prime minister is the 10th shortest in Australian history.
And it is shorter than the terms of either recent Labor leaders Kevin Rudd or Julia Gillard.
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