The Fort Worth Star-Telegram reports the deal is for one year and worth $4 million with $2.5 million guaranteed.
Clinton-Dix, who turned 27 in December, started all 16 games for the Bears in 2019 and finished the year with 78 tackles and two interceptions.
The Bears signed the veteran safety to a one-year, $3 million deal last spring, feeling he added veteran leadership to its secondary after former starting safety Adrian Amos departed for the Green Bay Packers in free agency.
The 21st overall pick of the 2014 NFL draft, Clinton-Dix spent five-plus seasons in Green Bay before being traded to the Washington Redskins during the 2018 season. Clinton-Dix was selected to the Pro Bowl in 2016 after co-leading all NFC safeties with five interceptions.
Clinton-Dix reunites with head coach Mike McCarthy, whom he played for in Green Bay.
Clinton-Dix has 522 tackles, 16 interceptions, 33 passes defensed, 4 forced fumbles and 5.5 sacks in six NFL seasons.
ESPN's Jeff Dickerson contributed to this report.