Azarov was endorsed by 252 votes in the 450-seat assembly.
Lawmakers from the opposition Batkivshchyna (Fatherland) party of jailed former Prime Minister Yulia Tymoshenko, the nationalist Svoboda (Freedom) party, and the Udar (Punch) party of boxing champion Vitali Klitschko did not take part in the vote.
Azarov, 64, has served as prime minister since Yanukovych became president in February 2010.
The vote on December 13 came at the end of a rowdy session that saw opposition and pro-government lawmakers exchange blows for a second day in a row in parliament.
The Party of Regions and its allies control a majority in parliament but opposition parties also made a good showing in Ukraine's October elections.