Turnbull, a multi-millionaire former banker and tech entrepreneur, won a secret party room vote by 54 to 44, Liberal Party whip Scott Buchholz told reporters after the meeting in Canberra.
Read: Australian PM Abbott faces new leadership challenge
Foreign Minister Julie Bishop was elected deputy leader of the party which, with junior coalition partner the National Party, won a landslide election in 2013.
Since then, the popularity of the government and Abbott in particular has suffered from a series of perceived policy missteps, destabilising infighting and leaks.
The opposition Labor Party has consistently led opinion polls, while Turnbull has been consistently viewed as preferred prime minister.
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