The Bears will send a sixth round pick in this year's draft to the Rams.
Jackson is scheduled to make $17.5 million in salary this season and the Rams will not be retaining any of his salary as part of the trade.
The trade cannot be officially processed until March 12.
Before playing for the Rams last season, Jackson spent four seasons with the Detroit Lions, where he went to the Pro Bowl in 2022. The trade also reunited Jackson with Bears new head coach Ben Johnson, who was previously an offensive coordinator with the Lions.