Vey, 22, played 18 games for Los Angeles last season and had five assists. He had 14 goals and 34 assists in 43 games for the Manchester Monarchs in the American Hockey League. Vey was a fourth-round pick (No. 96) by the Kings at the 2009 NHL Draft.
Los Angeles used the 50th pick to select defenseman Roland McKeown. The 18-year-old had 11 goals and 32 assists in 62 games for the Kingston Frontenacs in the Ontario Hockey League.
Prout, 24, had two goals and four assists in 49 games last season. He has three goals and 10 assists in 82 NHL games, all with Columbus.
Columbus' seventh pick (No. 154) at the 2010 NHL Draft, Prout has played in 117 American Hockey League games with the Springfield Falcons. He had seven goals, 18 assists and 138 penalty minutes.