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.
[He's] real confident with the puck now, getting it off his stick quick and no second-guessing. We need that. He's such a good guy in the room. He works so hard. That's the big thing. For not a big man, he just fights for every puck and when he scores, the guys appreciate that even more.
— Winnipeg Jets coach Paul Maurice on Mathieu Perreault, who scored two goals in win against Chicago Blackhawks on Tuesday