Assistants John MacLean and Dave Lewis also were fired and goaltending coach Greg Stefan was reassigned back to the team's pro scouting department.
Rod Brind'Amour, a third-year assistant who was the captain of Carolina's Cup-winning team, will remain part of the coaching staff, Francis said.
Muller was 80-80-27 in three seasons with the Hurricanes, who haven't made the playoffs since 2009, the longest active drought in the Eastern Conference. Carolina finished 13th in the 16-team East this season and has missed the postseason in seven of the eight years since winning its only Stanley Cup in 2006.
Muller, 48, made six All-Star teams during a 19-year career with six clubs, most notably New Jersey and Montreal.
He had never been a head coach in the NHL and was in his first season coaching the Milwaukee Admirals of the AHL when he was hired during the 2011-12 season to replace the fired Paul Maurice.
The relentlessly positive Muller spent the past month in limbo, saying in mid-April that upper management had not told him anything about his job status and that he was going about his business as if he would remain the coach.
While owner Peter Karmanos Jr. said late in the season that he liked the coaching staff, he added last week that any decision on Muller's fate would be entirely Francis'.
During his formal introduction as GM last week, Francis said his impending decision on Muller's status "needs due process."
Muller's final season was doomed by subpar years from the four highest-paid players on the roster forwards Alexander Semin and Eric and Jordan Staal, and goalie Cam Ward.
When Ward was asked during his exit interview if it was tough for Muller to get his message across in the dressing room, the goalie said "for me, obviously, I'm going to avoid that one."
MacLean, a teammate of Muller's in New Jersey and Dallas, and Lewis, a former head coach with three NHL clubs, each spent the past three seasons on Carolina's staff.
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