Tortorella was recently fired by the New York Rangers after they lost to the Boston Bruins in the NHL playoffs in five games.
The 55-year-old Tortorella replaces former Canucks coach Alain Vigneault, who took over as the Rangers' coach last week.
Tortorella has been a coach in the NHL since 2001. He led the Tampa Bay Lightning to the Stanley Cup championship in 2004.
As coach of the Rangers the past five seasons, Tortorella led New York to the playoffs three times.
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