Griese, 34, had two stints with Tampa Bay (2004-05, '08), and helped the Bucs win the 2005 NFC South division title.
The 6-foot-3, 214-pound Griese originally entered the NFL as a third-round pick with the Denver Broncos in 1998. He spent five seasons in Denver before joining Miami in 2003.
In his time away from Tampa Bay, Griese spent two seasons with the Chicago Bears (2006-07) before being traded back to the Buccaneers during the 2008 offseason.
Last year, Griese played in five games for the Bucs, completing 59.8 percent of his passes for 1,073 yards and tossing five touchdowns and seven interceptions.
Griese has completed 62.7 percent of his passes for 19,440 yards and thrown 119 touchdowns and 99 interceptions in 83 career starts.
Despite being the most experienced quarterback on Tampa Bay's roster, Griese did not appear to be in Tampa Bay's future plans at quarterback, where the Bucs will have four signal callers – Luke McCown, Byron Leftwich, Josh Freeman and Josh Johnson – compete in training camp.
Griese was, however, invited to Tampa Bay's mandatory mini-camp in June, but skipped those workouts as well as all voluntary practices during the offseason. It is believed Griese, who stayed in Denver to be with his pregnant wife for most of the offseason, was fined for missing Tampa Bay's mandatory mini-camp.