The 31-year-old left winger had 28 goals and 24 assists in 80 games last season.
"I never really thought about leaving," Burrows said. "All along, I always wanted to stay in Vancouver. As soon as the management showed interest in an extension, for me it was a no-brainer."
Burrows has spent his entire seven-year NHL career with Vancouver, totaling 139 goals and 131 assists in 522 games. He also has 16 goals and 12 assists in 58 career playoff games, including a club-record three goals in overtime.
"This is a core player who is a huge part of what we do and what we want to do going forward, and we couldn't be happier that he's going to be a Canuck for the next five years," assistant general manager Laurence Gilman said.
The deal came a day before the current collective bargaining agreement between the league and NHL Players' Association is set to expire.