Turnbull was sworn in by Governor-General Peter Cosgrove here, replacing Abbott who was ousted during a surprise ballot of his colleagues last night.
Soon after taking oath of office as the 29th Prime Minister of the country, the 60-year-old conservative leader vowed to bring a new style of consultative leadership to Australia.
"This is a turn of events I did not expect, I have to tell you, but it's one that I'm privileged to undertake, and one that I'm certainly up to," Turnbull told reporters here.
Turnbull said he would lead "a thoroughly Liberal government, committed to freedom, the individual and the market". He also said that parliament would serve its full term, implying no snap general election.
In the hastily-arranged late night party leadership ballot, 57-year-old Abbott received 44 votes against Turnbull's 54.
Multi-millionaire former banker Turnbull with strong backing from influential foreign minister Julie Bishop, who the party re-elected as deputy leader with a 70-30 vote in her favour, is expected to shake up the cabinet later this week.
Turnbull was ousted by Abbott as Liberal Party leader in 2009 over his support of the previous Labor government's carbon emissions trading scheme.
Abbott, who conceded that he had been ousted as a first- term prime minister after just two years in office, partly blamed internal "white-anting" and "character assassination" in the media for his demise, but promised not to "wreck" his Government in retribution.
He warned that the political instability in Australia will hurt the country's standing on the global stage.
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