Griese played college football at the University of Michigan from 1993 to 1997. Michigan did not offer him a scholarship, so he walked on to the football team. He turned down scholarship offers from Purdue and Kentucky. After he was redshirted in 1993 and limited to placeholding duties in 1994, Griese took over as the starting quarterback after Scott Dreisbach was injured five games into the 1995 season. Griese started for the remainder of the 1995 season, capped by an upset of #2 ranked Ohio State, 31–23.
At the beginning of the 1996 season, Dreisbach regained his starting job and Griese returned to the bench, serving as the team’s pooch punter. However, after Dreisbach struggled, Griese replaced him at halftime against Ohio State, where he led the Wolverines to another upset victory over the Buckeyes, 13–9. Griese finished the season starting in a 17–14 loss to Alabama in the Outback Bowl.
In 1997, Griese remained the starter. Along with Heisman Trophy winner Charles Woodson, he led the Wolverines to an undefeated season and the national championship. Griese was selected as the MVP of the 1998 Rose Bowl, passing for 251 yards and three touchdowns in Michigan’s win over Washington State.
In his Michigan career, Griese had a 17–5 record as a starter. The Wolverines won all three games against Ohio State in which he quarterbacked. He was inducted into the Rose Bowl Hall of Fame on December 30, 2012.