The move comes after the Lions attempted to sign tailback Malcolm Brown last month, but the Rams matched their offer sheet.
Anderson was a Pro Bowl selection in 2014 with the Broncos after tallying 849 rushing yards, 324 receiving yards and 10 total touchdowns. He originally joined the franchise as an undrafted free agent in 2013 out of California.
The Carolina Panthers and Oakland Raiders each waived Anderson last season. Following an injury to star running back Todd Gurley, who missed the Rams' final two regular-season games, Los Angeles signed Anderson.
Anderson exploded for 299 yards and two touchdowns in the Rams' last two games. He added 123 yards and two more scores in the NFC Divisional Round against the Dallas Cowboys.
In 69 career NFL games, Anderson has 760 carries for 3,454 yards and 22 rushing touchdowns. He has added 108 receptions for 900 yards and five receiving scores.