Griese, an 11-year veteran who played with Bucs coach Jon Gruden in Tampa in 2004-05, started six games for the Bears last season and had a 3-3 record. He took over for an ineffective Grossman in Week 4 and helped lead a comeback victory at Philadelphia. Griese suffered a left shoulder injury in November and never saw the field again.
Griese passed for 3,768 yards, 27 touchdowns and 19 interceptions in his two seasons in Tampa. His 97.5 quarterback rating in 2004 is the best single-season mark in Bucs' history.
The Associated Press contributed to this story.