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.
There's no discouragement in that room. There's no issues there at all to be honest with you. It's more about, 'Hey, it's opportunities for players.' And if we become that bad of a team because of one player, it's not a real good sign for our hockey club. So this is part of sports. It's part of hockey.
— Bruins coach Claude Julien on the loss of Zdeno Chara to injury