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.
"Today we are making an important change in the direction of our team," said Linden. "On behalf of the entire organization, we extend our thanks to John, Mike and their families for their commitment to the Canucks and wish them the very best.
"We have a lot of important work to accomplish this off-season as we build our management and coaching staff, improve our roster and connect with our fans. Our General Manager search is well underway and we will begin assessing head coaching candidates immediately."