Toronto was 9-1-2 in its last 12 games and finished 41-33-8, good for ninth place in the Eastern Conference.
"This change is much about the future and where we're going as an organization, as much as it is what has transpired here," said General Manager John Ferguson on the team's Web site.
Quinn, 63, has missed the post-season just four times in 19 years as a head coach. He guided Toronto to the Eastern Conference finals in the 1998-99 and 2001-02 seasons, and is fourth in NHL history with 657 all-time coaching victories behind Scotty Bowman (1,244), Al Arbour (781) and Dick Irvin (692).
He coached Team Canada to the 2002 Olympic gold medal and to the gold in the 2004 World Cup of Hockey.