Darryl Sutter has a new right-hand man.
Muller served as the associate coach with the Montreal Canadiens for the past five seasons. He was fired along with head coach Claude Julien on Feb. 24. He was the head coach of the Carolina Hurricanes for parts of three seasons from 2011 to 2014.
The 55-year-old recorded 959 points in 1,349 games during his 19-year playing career, winning a Stanley Cup with the Habs in 1993.
Calgary is also promoting Cail MacLean from head coach of the AHL's Stockton Heat to an assistant coach with the Flames.
Former assistants Martin Gelinas and Ray Edwards won't return to the coaching staff. Both will stay with the organization in player development roles, though.
Sutter replaced Geoff Ward behind the bench midway through the 2020-21 campaign, going 15-15-0.