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 a winner. We want winners here, and he's a proven winner. He's won two Stanley Cups. He's 22 years old and been a big part of it. He's got all the right tools. He's got size (6-foot-1, 204 pounds) and strength. He's exactly what we were looking for. He's going to be a big piece of our team for many, many years to come.
— Blue Jackets GM Jarmo Kekalainen on Brandon Saad, who he acquired in a trade with the Blackhawks on Tuesday