Verlander, also named the American League's Most Outstanding Pitcher, had a career year as the ace of a formidable Tigers staff. He finished with a record of 24-5, 250 strikeouts and a career-low earned run average of 2.40.
He led the Tigers to a 95-win season and their first division title since they won the AL East in 1987.
Kershaw's teammate, center fielder Matt Kemp, was honored as the NL's Most Outstanding Player.
Kemp posted a .324 batting average while pacing the NL in home runs (39), RBI (126) and runs (115). He became the first-ever Dodger to take home the Most Outstanding Player award.
Yankees outfielder Curtis Granderson was named the AL's Most Outstanding Player.
Granderson batted .262 with a career-high 41 home runs, 119 RBI and 25 stolen bases in 156 games for the Yankees, who finished with the best record in the American League at 97-65, but were bounced from the playoffs in the divisional round by the Tigers.
Texas' Michael Young captured the Marvin Miller Man of the Year Award.
The award, named for the founding executive director of the MLB Players Association, is awarded to the player "whose on-field and off-field performance most inspires others to higher levels of achievement by displaying as much passion to give back to others as he shows between the lines on the baseball diamond."
Young, who batted .338 with 106 RBI for the AL champion Rangers this season, also took home the award in 2008.
Ellsbury, limited to just 18 games in 2010 due to fractured ribs, established career highs in games played (158), runs (119), home runs (32) and RBI (105).
Berkman, 35, returned from 2010 knee surgery to bat .301 with 31 home runs and 94 RBI for the World Series champion Cardinals.
The Players Choice Awards are unique because the electorate consists of the players themselves. Balloting for the awards, presented annually since 1992, was conducted in September.