The 29-year-old native of New Westminster, B.C., captured the award Thursday at the CFL awards banquet.
Linebacker Henoc Muamba of the Winnipeg Blue Bombers was the other finalist in voting conducted by the Football Reporters of Canada and eight CFL head coaches.
Cornish has also been nominated for the CFL's outstanding player award along with Toronto Argonauts quarterback Ricky Ray.
The six-foot, 217-pound Cornish ran for a CFL-high 1,813 yards, the most in a season by a Canadian, and also led the league in yards from scrimmage (2,157) and TDs (14) as Calgary (14-4) finish atop the West Division.
The six-foot, 230-pound Muamba, taken first overall in the 2011 CFL draft, was a bright spot for Winnipeg (3-15). The former St. Francis Xavier star finished second overall in tackles (106) and added 18 special-teams tackles, a sack and interception.
Muamba, 24, was born in Zaire (now the Democratic Republic of the Congo) but grew up in Mississauga, Ont. He also was Winnipeg's selection as outstanding player and top defensive player and is slated to become a free agent this off-season.