Terms of the deal with Thomas weren't disclosed.
Thomas is a 13-year NFL veteran who played the last three seasons in New Orleans. He spent his first 10 seasons with the Philadelphia Eagles after signing as an undrafted free agent in 1996, and he has started 123 of 162 career games and recorded 20 sacks.
Thomas missed the first half of last season after hurting a triceps muscle during training camp. He was released in September with an injury settlement and re-signed in November, totaling 10 tackles in the final eight games.
The Rams also waived defensive linemen Kirston Pittman and Willie Williams on Wednesday, along with wide receivers Travis Brown and Horace Gant.
The Associated Press contributed to this report.