won the Liberal Party room vote 54-44 in Canberra, hours after declaring his leadership bid.
A former lawyer turned businessman, Turnbull told a late-night press briefing that his new government would be "thoroughly consultative."
"The prime minister of Australia is not a president. The prime minister is the first among equals," he said, flanked by Julie Bishop, who was returned as the party's deputy leader.
The remark could be seen as a criticism of Abbott's leadership style. He was considered a leader prone to making "captain's calls" -- decisions made without any consultation.
Turnbull wouldn't comment on any departures from current government policy, saying that any decisions would be made in a "thoughtful and considered manner."
"I'm not going to make policy pronouncement from this podium tonight. Of course policies change, they change all the time," he said.
Abbott seemed caught off guard by the swift pace of the leadership challenge, though rumors -- and low ratings in polls --had suggested his position was in trouble for months.
In a hastily convened press conference Monday afternoon, Abbott said: "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."
Not the first challenge
In February, Abbott emerged victorious from a no-confidence vote among his party colleagues, with 61 votes to 39. The Prime Minister may have won majority backing, but the 39 votes against him left him exposed and at risk of further insurrections.
Abbott came to power in 2013 with the promise of a stable government, immune from the infighting that had dogged the previous Labor leadership. During the previous government, Kevin Rudd and Julia Gillard jostled for the top job, and the Liberal Party rightly identified that the electorate had had enough.
However, a series of unpopular decisions exposed cracks within the Liberal Party. Abbott was seen to have bungled his first budget, which went down badly with voters. The Liberal Party had sold itself as old hands when it came to managing the country's economy, capable of correcting lax Labor spending, which had eroded a surplus deftly created by the former Liberal government, led by John Howard.
Basis of challenge
On Monday, Turnbull's nomination speech pulled Abbott up on his economic record.
"It is clear enough that the government is not successful in providing the economic leadership that we need," he said. "He has not been capable of providing the economic confidence that business needs."
Abbott defended himself against the attack by drawing on the government's successes.
"Since coming to Government, our team has stopped the boats, improved the budget, cut taxes and increased jobs. We have laid the foundation for a better deal for families and for small business.
"You can trust me to deliver a stronger economy and a safer community," he said.
Since coming to power Abbott has prided himself on his tough stance on immigration. His "Stop the boats" campaign sought to end the flow of migrants to Australian waters.
His government said it was saving lives at sea, but the operational silence that surrounded the policy attracted criticism, not the least from human rights advocates who accused Australia of breaking international law.
Opposition scare tactics
Turnbull warned that if Abbott continued to lead the party it was likely to lose the next election to Labor and its leader Bill Shorten.
"You only have to see the catastrophically reckless approach of Mr. Shorten to the China-Australia free trade agreement,
surely one of the most important foundations of our prosperity, to know he is utterly unfit to be Prime Minister of this country and so he will be if we do not make a change," Turnbull said.
The Australian economy has been feeling the effects of slowing demand from China for minerals. Australia's gross domestic product expanded 0.2%
in the second quarter, down from 0.9%, missing analysts' forecasts.
Shorten said a change at the top of the Liberal Party wouldn't make any difference.
"Australia does not need another out of touch, arrogant, Liberal leader. Australia needs a change of government," he said.
Abbott losing support
The most recent survey by Newspoll -- as of September 7
-- shows voters are split between the two major parties, though respondents said Shorten would make a better leader than Abbott.
Until Monday, Turnbull was the country's popular communication minister, someone seen by many as a potential leader, if only he'd put up his hand. In February, he resisted pressure to be nominated for the role during the party-room vote.
In the past, Turnbull has expressed support for same-sex marriage and concern that not enough is being done to combat climate change.