The contract includes $18 million in guarantees, according to the source. The league year and the free-agency period begin at 4 p.m. ET Wednesday.
For the most part, Amukamara, who was paid $7 million guaranteed by Chicago on a one-year deal in 2017, worked out for the Bears, playing adequately enough to start 12 games. He finished second on the Bears' defense with seven pass breakups, behind only fellow free-agent cornerback Kyle Fuller (22).
However, Amukamara, 28, failed to intercept a pass for the second consecutive season, and his inability to take the ball away is probably his biggest downside.
Before joining the Bears, Amukamara spent five seasons with the New York Giants (2011 to 2015) and one year in Jacksonville (2016). He missed 27 games with various injuries from 2011 to 2016, including 13 games in the 2014 and 2015 seasons.
In his career, Amukamara has seven interceptions, 58 pass breakups and three forced fumbles in 83 games.
ESPN's Jeff Dickerson contributed to this report.