Sims, 29, has been the rare former Rams draft pick to stick with the team for multiple contracts as he developed into a key piece in the defensive line's rotation.
In 2015, Sims started nine games, posting 24 tackles, 1.5 sacks, a forced fumble, a fumble recovery and an interception he almost returned for a touchdown in the season finale.
After the season, Sims made it clear he wanted to return to the Rams, even if it meant continuing in a backup role.
In six seasons with the Rams, Sims has played in 83 games with 111 tackles, 9.5 sacks, two interceptions, a forced fumble and three fumble recoveries.
The Rams drafted Sims out of West Texas A&M in the sixth round of the 2010 draft.