Clinton-Dix, 26, spent the final nine games last season with the Washington Redskins after he was acquired in a trade with the Green Bay Packers. He became an immediate starter, replacing Montae Nicholson, and finished with 65 tackles and three pass breakups.
He struggled at times with Washington, but coaches liked his communication skills and he has big-play ability.
His agreement with the Bears, first reported by the NFL Network, comes after the team lost starting safety Adrian Amos to the Packers in free agency. Amos signed a four-year deal worth $37 million in Green Bay.
Clinton-Dix has 14 career interceptions, all with Green Bay, where he had been a starter since his rookie season and was selected to the Pro Bowl in 2016. He had three interceptions in seven starts with the Packers before the midseason trade to the Redskins.
The 2014 first-round pick (21st overall) once had a streak of 2,033 consecutive defensive plays on the field while with the Packers.
NFL Network reports that Clinton-Dix signed for $3.5 million. Clinton-Dix was offered more elsewhere, the network reported, but wanted to join Bears Pro Bowl safety Eddie Jackson -- his former teammate at Alabama -- in Chicago.
ESPN's John Keim contributed to this report.