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.
This team has been a real treat to say you've been the head coach of them. I'm extremely proud of this group ... after the disappointment of (the Game 6 loss) is digested, it's always a lot easier as a coach when your team has emptied its tank, and that team emptied its tank for me for three months.
— Senators coach Dave Cameron after getting eliminated in the first round by the Canadiens