The deal will put Davis under team control until 2017, despite not yet playing in a game for the Browns.
Davis, 26, signed with the Rams in 2012 as an undrafted free agent, and made eight starts for St. Louis last year. He threw for 2,001 yards and 12 touchdowns before the Rams cut him in the off-season.
The Browns have dealt with injuries to their quarterbacks this season, with Josh McCown sustaining a concussion in Week 1 against the Jets and Johnny Manziel dealing with elbow soreness during the preseason. McCown was cleared to play before last Sunday’s 27–20 loss to the Raiders, and Manziel’s elbow wasn't an issue in the single start he made for Cleveland this year.
The Browns (1–2) will play the Chargers (1–2) in Week 4.
- Erin Flynn