Philadelphia, in 10th place in the Eastern Conference with a 13-11-1 record, have lost three successive games and six of their last seven.
"This was a very difficult decision for me to make, given my relationship with John," Holmgren said in a statement on the Flyers' website (http://flyers.nhl.com).
"In watching the team over the past few weeks I felt a new voice was needed in order to get us out of this and in the direction we expect."
Stevens, hired by the Flyers in 2006, went 120-109-34 and had two 10-game losing streaks.
"Obviously this is a great opportunity," said Laviolette, whose first game in charge will be on Saturday against visiting Washington.
"I am really excited. The Flyers are an organization that has a lot of tradition and a lot of history."
(Writing by Steve Ginsburg; Editing by Patrick Johnston; To query or comment on this story firstname.lastname@example.org)