Waite held the position since 2013. He joined the Canadiens after winning Stanley Cups with the Chicago Blackhawks in 2010 and 2013 and worked closely with Carey Price during the prime of his career.
The Canadiens hired Burke as a scout in 2016. He also spent six seasons with the Arizona Coyotes in a variety of roles, including assistant general manager. He had an 18-year NHL career as a netminder and was GM of Canada's 2018 Olympic team.
Burke needs to quarantine for 14 days before he can join the team.
Montreal fired former head coach Claude Julien and assistant Kirk Muller last week. The team named Dominique Ducharme its new bench boss on an interim basis.
The Canadiens' goaltending has been a focal point amid the club's recent slump, as Price has posted an .888 save percentage in 12 appearances this season. Jake Allen has registered significantly superior stats in the backup role.