Griffin became the first Baylor Bear to win the award, indicative of college football's top player.
The junior signal-caller threw for 3,998 yards and 36 touchdowns this season while running for 644 yards and nine more scores for the 15th-ranked Bears (9-3).
Luck, meanwhile, lost for the second time in two years as a Heisman finalist. Auburn quarterback Cam Newton edged him for last year's award.
The junior, who plans to turn pro next year, racked up 3,170 yards and 35 touchdowns for fourth-ranked Stanford (11-1), which will play No. 3 Oklahoma State in the Fiesta Bowl.
Running backs Trent Richardson of Alabama and Montee Ball of Wisconsin and versatile LSU cornerback Tyrann Mathieu were also among this year's finalists.