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.
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.
