Applebaum succeeds Gerald Tremblay, who resigned under pressure amid allegations he ignored illegal party fundraising, the Canadian Broadcasting Corp. reported Friday.
No charges have been brought against Tremblay, the CBC said.
Applebaum is to hold the office until the next election, in November 2013.
"Now is the time to re-establish our bridges, to work together and to ensure that Montrealers can be proud of what we do as elected officials," Applebaum said after the council vote.
Applebaum's city council seat will not be filled until the next municipal election, the CBC said.