The 22-year-old Vey had five assists in 18 games for Los Angeles last season.
He had 55 goals and 103 assists over three season with the Manchester Monarchs, the Kings' American Hockey League affiliate.
Vancouver acquired the 50th pick in a trade with the Tampa Bay Lightning on Friday. The Canucks sent defenceman Jason Garrison, the rights to forward Jeff Costello and a seventh-round pick in the 2015 NHL Draft to Tampa in return.
Unless he really collapses, I don't see him going anywhere. I've been very impressed with his composure and maturity. Once the regular season started, he was a different guy; it was like game on and almost as if he's been around for a long time.
— Florida Panthers general manager Dale Tallon on rookie defenseman Aaron Ekblad