Linebacker Luke Kuechly, who led the NFL in tackles (164) and started all 16 games for the Carolina Panthers, grabbed the award for defensive rookies.
Griffin beat quarterbacks Andrew Luck of the Indianapolis Colts and Russell Wilson of the Seattle Seahawks, and Redskins running back Alfred Morris for the award.
Griffin threw for 3,200 yards and 20 touchdowns while completing 65 percent of his passes but his threat to run the ball confounded defenses all season.
He rushed for 815 yards and seven touchdowns while leading the Redskins to a 10-6 record.
The 22-year-old former Heisman Trophy winner out of Baylor said leading the Redskins back to the playoffs was his proudest accomplishment.
"Being the NFL East champions, that was the highlight for me," Griffin, the number two pick in the NFL Draft, said after winning the award at the NFL Honors ceremony at the Mahalia Jackson Theater in New Orleans.
"When we were 3-6 and we had to win, we did," he told reporters. "To have the last game in our house (against Dallas) on national TV, the bright lights, and come away with the victory, that showed a lot of character for our football team."
The Redskins beat the Cowboys 28-18 to win the NFC East and reach the postseason but they lost the following week at home in the playoffs to the Seattle Seahawks 24-14.
Griffin injured his right knee against the Seahawks and underwent surgery on Jan. 9. He said the rehabilitation was already ahead of schedule.
Kuechly started the season on the weak side of Carolina's 4-3 defense, but he moved to the middle after Jon Beason was lost for the season with knee and shoulder injuries.
"I've got a great d-line in front of me they help me play, helped me stay uncovered a lot," said Kuechly who was drafted ninth overall out of Boston College.
He said the switch to middle linebacker was key to his strong season.
"It was more of a comfort thing, it's where I played in college," he said. "After that first game at middle linebacker (against Seattle in Week 5) I thought, 'this feels better, feels more comfortable'."
The awards were selected by a panel of NFL reporters in a poll conducted by the Associated Press.
