Maurice was in his second stint with the franchise and served 920 games behind the bench for the organization. He had a record of 384-391-145 during his tenure.
Muller will take over a Hurricanes team that is last in the Southeast Division with a record of 8-13-4. Only the New York Islanders have fewer points in the Eastern Conference.
"Kirk is a proven leader and motivator, and he has strong communication skills," said Hurricanes president and general manager Jim Rutherford in a statement. "He was a captain and a Stanley Cup winner as a player, and did excellent work as a coach with the Canadiens and the Admirals. We feel confident that he is the right man to lead our team now and in the future."
Muller was in his first season with Milwaukee, which was 10-6-0 entering Monday. He had served as an assistant coach with Montreal for five seasons and was a head coach on the Canadian collegiate level.
A six-time All Star during his playing career, Muller was selected by New Jersey with the second overall pick of the 1984 draft -- behind only Mario Lemieux -- and skated in 1,349 games with the Devils, Canadiens, Islanders, Maple Leafs, Panthers and Stars. He compiled 357 goals with 602 assists for 959 points and won a Stanley Cup with Montreal in 1993.
Maurice was the first head coach of the Hurricanes after the team moved from Hartford for the 1997-98 season, having taken charge of the Whalers in November 1995 at the age of 28. He was fired 30 games into the 2003-04 season, then coached for two seasons with the Maple Leafs before returning to the Hurricanes in December 2008 when Peter Laviolette was fired.
After leading the Hurricanes to the Eastern Conference finals in the spring of 2009, Maurice was rewarded with a three-year contract that was set to expire after this season. The team failed to qualify for the playoffs in each of the past two seasons before this year's miserable start.
Maurice is the all-time winningest head coach in franchise history. He guided the team to the Eastern Conference title in 2002 and a pair of Southeast Division titles.
The Sault Ste. Marie native owns a career coaching mark of 460-457-167. In his two-year run with Toronto, he posted a mark of 76-66-22, but the Leafs failed to reach the playoffs both years.