The 31-year-old Griese completed 112-of-174 passes for 1,136 yards and led Tampa Bay to a 5-1 start last year before a season-ending knee. The Buccaneers decided to waive him this month rather than pay a $2.6 million roster bonus.
Griese has passed for 16,344 yards and 103 touchdowns in eight seasons with Denver, Miami and Tampa Bay.
The Bears have said they are committed to Rex Grossman as their starter, but Griese has started 72 of 75 games in his career.
