Quessenberry, 34, most recently played for the Vikings, where he played in 33 games (four starts) over the last two seasons.
Overall, he has started in 30 of 84 career games played through seven seasons, including stints with the Houston Texans (2017), Tennessee Titans (2018-21), Buffalo Bills (2022) and Minnesota Vikings (2023-24).
The 6-foot-5, 310-pound offensive lineman originally entered the NFL as a sixth-round draft pick by the Texans out of San Jose State in 2013.
The Rams on Thursday signed offensive tackle David Quessenberry to a one-year deal.