"Alex plays with intensity and determination at both ends of the rink," said Canucks' general manager Mike Gillis. "He's a fierce competitor and a versatile player. We look forward to further growth and development in his game."
In his fourth season, the Pincourt, Quebec native is in the midst of a breakout campaign. He has already eclipsed his career highs in goals (19) and points (33).
With Burrows signed, the Sedins and defenseman Mattias Ohlund loom as the most important of Vancouver's upcoming free agents.
Burrows was slated to be an unrestricted free agent July 1.
ESPN.com's Pierre LeBrun contributed to this report.