The deal was announced Thursday. Bronson tried out with the Bears at this week's voluntary minicamp.
An undrafted free agent out of McNeese State, Bronson entered the NFL in 2013 and spent that season on Kansas City's practice squad. He was released before the 2014 regular season.
Bronson played in 40 games in college and had 230 tackles, 10 interceptions, three forced fumbles and two fumble recoveries.
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