Terms of the deal were not disclosed.
Rypien, a fifth-year pro, joins a position group that includes veteran starter Matthew Stafford and rookie Stetson Bennett, a fourth-round pick in last week’s NFL draft.
Rypien, 26, played at Boise State and signed with the Denver Broncos as an undrafted free agent in 2019. In eight games, including three starts, he passed for four touchdowns, with eight interceptions.
Coach Sean McVay now has a full complement of quarterbacks as the Rams attempt to rebound from last season’s 5-12 finish, the worst season-after performance by a Super Bowl champion in NFL history.
The Rams did not re-sign backups John Wolford and Bryce Perkins, who remain free agents.
Stafford, 35, last season played through right elbow tendonitis, was sidelined for a game because of a concussion and sat out the final seven games because of a spinal bruise.
Stafford, preparing for his 15th NFL season, said at the start of offseason workouts that he felt fine and, unlike last offseason, he is throwing passes during drills.
Bennett, 25, led Georgia to back-to-back national titles.