Tampa Bay also receives the rights to forward Jeff Costello and Vancouver's seventh round draft pick in 2015, while the Canucks will receive the 50th overall pick in tonight's NHL draft.
Garrison, 29, signed a six-year contract worth $27.6 million with the Canucks in 2012. He played 81 games for Vancouver last season, totaling 26 assists and seven goals.
This is the Canucks second trade of the day. The team traded Ryan Kesler to the Anaheim Ducks earlier on Friday.