"I would like to sincerely thank Claude and Kirk for their contributions to our team over the past five years," said Canadiens general manager Marc Bergevin in a news release.
Our team can achieve high standards, and the time had come for a change.
Canadiens general manager Marc Bergevin
"I have great respect for these two men whom I hold in high regard."
The announcement marks the end of Julien’s second stint as head coach of the team. He had been at the helm since taking over from Michel Therrien midway through the 2016-2017 season. He also coached the Habs from 2002-03 to 2005-06.
Muller has served as assistant coach since 2016 and won the 1993 Stanley Cup with the team as a player.
After a strong start to the season, the Habs are fourth place in the North Division and winless in their last three games following a shootout loss to the Ottawa Senators on Tuesday.
Dominique Ducharme has been promoted to interim head coach and Alex Burrows has joined the coaching staff.
"In Dominique Ducharme, we see a very promising coach who will bring new life and new energy to our group," said Bergevin. "We feel that our team can achieve high standards and the time had come for a change."
A native of Joliette, Ducharme, 47, has served two seasons as an assistant coach with the Canadiens.
Bergevin and Ducharme will speak to the media this afternoon when the team arrives in Winnipeg for a game on Thursday.