Bradbury, 30, is due $3.7 million this upcoming season before becoming an unrestricted free agent. He's coming off a season where he didn't commit a single penalty or allow a sack.
The now eight-year vet allowed four quarterback hits and 20 pressures on 642 pass blocking snaps. However, his 51.6 run blocking grade was the lowest of his career.
Bradbury, who has played in all 17 regular season games in back-to-back years, is set to replace Drew Dalman, who surprised the league after announcing his retirement following his first season with the Bears.
He spent the first six years of his career with the Minnesota Vikings after they drafted him with the 18th overall pick in the 2019 NFL Draft.