Anderson previously played five seasons with the Denver Broncos before being released in April.
Anderson rushed for a career-high 1,007 yards in 2017, when he started all 16 games for the Broncos. He also had 40 receptions for 224 yards.
With the Panthers, he is expected to provide a complement to Christian McCaffrey, who has varied skills but may not be an every-down back.
"As far as ground and pound, the Keep Pounding slogan that Carolina likes to [use], the ground and pound game I think fits [me] well," Anderson said Monday, per the Charlotte Observer. "Breaking tackles and finding ways to use that to make long runs and bigger plays, also catching the ball out of the backfield, too.
"But having a guy like McCaffrey, who's super shifty and also can do some of the same things, it can be a great complementary [relationship] with each other."
Panthers general manager Marty Hurney pointed out after the draft that the team had not addressed its need for a power back.
"Not so far," Hurney said then, according to Bill Voth on the Panthers' website. "Again, that's something that we keep looking at and we'll continue to look at."
During his five-year NFL career, Anderson, 27, has 3,051 rushing yards, 20 rushing touchdowns, 103 receptions, 559 receiving yards and four touchdown catches.
He has also rushed for 323 yards in five postseason games.
He was named to the Pro Bowl in 2014 when he had 849 rushing yards and 324 receiving yards.
Anderson was signed by the Broncos as a free agent out of Cal in 2013.