Coach Jeff Fisher reportedly notified his team about the change at a team meeting on Wednesday.
Hill became the team's starter after Sam Bradford was lost for the season with an ACL tear.
In last week's loss to the Arizona Cardinals, Davis completed 17 of his 30 pass attempts for 216 yards with one touchdown and two interceptions. The previous week, Davis threw for only 102 yards with a touchdown and two interceptions.
The Rams, who rank 26th in the league with 212.8 passing yards per game, are 3-6 this season and in last place in the NFC West.
- Chris Johnson