The Chargers confirmed that Brown agreed to terms on a three-year deal to join the team on Tuesday, the opening day of NFL free agency.
Brown agreed to a three-year, $10.5 million deal, which includes $4 million guaranteed money, according to the U-T San Diego. Mathews, 26, is set to make close to $2 million in base salary for the upcoming season.
Brown, 26, finished with 537 yards and six touchdowns, averaging 5.3 yards per carry for the Colts in 2013. Even with Indianapolis making a midseason trade with Cleveland for Trent Richardson, Brown was the more effective back.
Brown also is a good fit for San Diego's zone running scheme, with his one-cut, downhill running style. Chargers general manager Tom Telesco has some familiarity with the Connecticut product, having worked in the personnel department for the Colts when Indianapolis selected him in the first round of the 2009 draft.
The Chargers were looking for someone to serve as a backup for Mathews, who finished with a career-high 1,255 yards in last season, but wore down in the playoffs.