Anderson is expected to provide depth at his position through the final two regular-season games and playoffs with fellow running back Todd Gurley being considered day-to-day because of inflammation in his knee.
While Gurley downplayed the situation, coach Sean McVay told reporters earlier this week that he wants his star running back to play in the final two games for the Rams (11-3). Los Angeles, which has clinched the NFC West, faces the division-rival Arizona Cardinals (3-11) and San Francisco 49ers (4-10) to wrap up the regular season.
"If he's able to go, we want him to be able to go," McVay said. "But if it's something that whether you're playing for the playoffs or whether you're not, we're always going to be smart with a player like Todd."
Anderson joins second-year pro Justin Davis and rookie John Kelly as backups to Gurley.
The 27-year-old Anderson spent a week with the Oakland Raiders earlier this month without playing in a game before being released.
Anderson was released by the Carolina Panthers on Nov. 12, mere months after signing a one-year, $1.75 million contract with the club. He had 104 yards on 24 carries this season to go along with one reception that went for 24 yards and a touchdown.
Anderson, who spent his first five seasons with the Denver Broncos (2013-17), had visited the Kansas City Chiefs in the wake of Kareem Hunt's release. Former Chiefs running back Charcandrick West re-signed with the team to replace Hunt, who was released by the club after a video showed him pushing and kicking a woman in February.
Anderson was a Pro Bowl selection in 2014, and he rushed for a career-high 1,007 yards for the Broncos last season, when he started all 16 games.
For his career, Anderson has 717 carries for 3,155 yards and 20 touchdowns. He has totaled 104 receptions for 883 yards and five touchdowns.
Cooper initially was placed on injured reserve after he underwent ankle surgery following a season-opening 33-13 victory over the Oakland Raiders. He returned two punts for 12 yards and three kickoffs for 75 yards against the Raiders.
The 23-year-old was activated in Week 11 and took over as kickoff returner, while JoJo Natson remained as punt returner.
Cooper led the league with 27.4 yards per kick return and finished second in punt return average at 12.5 in 2017.
The 5-foot-11, 208-pound Cooper has 25 receptions for 190 yards in 26 career contests since being selected by the Rams in the fourth round of the 2016 NFL Draft.