Terms of the deal haven't been disclosed. ESPN first reported the news.
Christian, 25, will be suspended for the first two games of the regular season, ESPN reported in June. The reason for that suspension hasn't been made clear.
Christian played in 55 games for the Rams over the past four seasons, starting once. He offers the Bears another option at safety alongside Eddie Jackson in addition to potentially working on special teams.
Christian played in 34% of the Rams' snaps on defense and 79% of their snaps on special teams in 2019.
The Bears are conducting an open competition for the safety spot alongside Jackson, a two-time Pro Bowl selection. Veteran free-agent addition Tashaun Gipson, 30, is considered the frontrunner to earn the starting role. Deon Bush is also in the competition.
The Bears haven't yet made Christian's signing official. As part of the physical process, he must take a coronavirus test and quarantine before those results return.