The 29-year-old native of New Westminster, B.C., received the league's top individual honour Thursday at the CFL awards banquet.
Cornish becomes just the third Canadian to capture the honour and first since '78 when tight end Tony Gabriel of the Ottawa Rough Riders claimed it.
Russ Jackson, the legendary Ottawa quarterback, was a three-time outstanding player award winner (1963, '66, '69).
Toronto Argonauts quarterback Ray was the other finalist in voting by the Football Reporters of Canada and eight CFL head coaches.
Earlier on Thursday, Cornish was named the league's top Canadian for the second straight year.
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.
Ray, 34, enjoyed a record-setting second season with Toronto. The California native had a CFL-record 77.2 per cent completion average and just two interceptions in 303 pass attempts to become the first player to have an interception percentage under 1.0 (0.7).
However, Ray only appeared in 10 regular-season games, missing seven starts due to injury before being a healthy scratch in Toronto’s regular-season finale.