The Carolina position will be the first NHL head coaching post for Muller, 45, who most recently coached the Milwaukee Admirals of the American Hockey League. He's also been an assistant on the Montreal Canadiens since retiring as a player after the 2002-03 season.
Muller, a center as a player, broke into the NHL in the 1984-85 season with the New Jersey Devils. He also played for Montreal, the New York Islanders, Toronto, Florida and Dallas. He appeared in 1,349 regular-season games, scoring 357 goals and assisting on 602 others.
He was part of the Canadiens team that won the Stanley Cup in 1993.
"Kirk is a proven leader and motivator, and he has strong communication skills," Hurricanes President and General Manager Jim Rutherford said.
"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."
Maurice was in his third season of a second stint as coach of the Hurricanes when he was fired Monday. He coached the franchise from the 1995-96 season through 2003-04, a period that included the team's move from Hartford to Carolina, and again from 2008-09 until Monday. He also coached the Toronto Maple Leafs for two seasons.
Maurice was 384-391-145 in his two tenures with the Hurricanes. Carolina is 8-13-4 this season. Its 20 points is the second-lowest in the NHL Eastern Division.
The Hurricanes have missed the playoffs each of the last two seasons.
Maurice was the second NHL coach fired Monday and third this month. The Washington Capitals removed Bruce Boudreau Monday and replaced him with former Capitals player Dale Hunter, while the St. Louis Blues dumped Davis Payne for Ken Hitchcock Nov. 6.