Price trailed Boston's Jon Lester until the final week of the season in the award's point system, which evaluates pitchers based on wins, strikeouts and ERA.
Lester gave up eight runs in his final start of the season against the Chicago White Sox, failing in his bid to become the first Red Sox left-hander in 57 years to win 20 games.
That allowed Price to move ahead. The AL starter in this year's All-Star game finished 19-6 with a 2.72 ERA and 188 strikeouts.
Price has been invited to accept the award at a gala in Oklahoma City in January.
CC Sabathia of the New York Yankees won it the past two years.