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 only 17 but he can see the ice so well and he moves the puck and goes to the open ice all the time, so I just think he's a player that is ready to play in the NHL. I'm really looking forward to coaching someone like this.
— U.S. National Junior Team coach Ron Wilson on Auston Matthews, the projected No. 1 pick of the 2016 NHL Draft