Financial terms were not disclosed, but ESPN reported the deal is worth $4.5 million and includes a $1.25 million signing bonus.
The contract also includes an escalator clause based on playing time that could increase the value of the contract to $7.8 million, ESPN said.
Chandler, 36, spent the last five seasons with the Atlanta Falcons but was waived in a salary cap move. The Falcons also are turning to Michael Vick, last season's top overall draft pick, at quarterback.
With a history of concussions and other injuries, Chandler likely will back up Jim Miller with the Bears, who won the NFC Central Division title last season for the first time since 1990 despite inconsistent play at quarterback.
In his final season in Atlanta, Chandler passed for 2,847 yards with 16 touchdowns and 14 interceptions while playing behind an offensive line that yielded 41 sacks.
Chandler, who has been among the NFL's better quarterbacks when healthy, enjoyed his shining moment in 1998, leading the Falcons to Super Bowl XXXIII, where they were beaten by Denver.
Entering his 15th season, Chandler will be joining his seventh team. In 158 games, including 137 starts, the two-time Pro Bowler has passed for 25,948 yards and 161 touchdowns with 127 interceptions.
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