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.
You know what? We've played in some pretty special buildings along this playoff run so far. You start in Detroit, you go to Montreal, you come here … I think it's the first team to beat three Original Six teams to get to the Final if I'm not mistaken. That says how tough the road has been. Those are tough places to win.
— Lightning forward Steven Stamkos after Game 7 win vs. Rangers on Friday in New York