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.
Rosie O'Donnell unveils nearly 50-pound weight loss
Justin Bieber crashes Drake Bell's album release party