Tortorella, hired to coach the Canucks on June 25, 2013, was in the first year of a five-year, $10 million contract.
He guided the Canucks to a 36-35-11 record this season, missing the playoffs.
In parts of 14 NHL seasons coaching the Tampa Bay Lightning, where he won the Stanley Cup in 2004, New York Rangers and Canucks, Tortorella has compiled a 455-367-37-82 record.
Tortorella won the Jack Adams Award as Coach of the Year during the 2003-04 season.
A replacement is not expected to be named until the Canucks hire a new General Manager.