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.
We think that Randy is a very good coach. Our players think that Randy is a very good coach. We think that he's going to get the most out of this group. With the addition of the two assistants, a bit of a different dynamic, we're very comfortable that this is a quality coaching staff that's going to maximize the potential of this team.
— Maple Leafs GM Dave Nonis on head coach Randy Carlyle and his staff