The deal includes a reported $250,000 in bonuses and guarantees.
The 5-foot-10, 207-pound Brown joins a New England running back group that includes Dion Lewis (recovering from a torn ACL), James White, Tyler Gaffney, Joey Iosefa and Brandon Bolden.
Brown originally entered the NFL as a first-round pick (27th overall) by the Colts out of Connecticut in the 2009 NFL Draft. He signed with the Chargers as an unrestricted free agent March 11, 2014.
Brown has played in 89 NFL games (25 starts) and has 695 rushing attempts for 2,829 yards and 18 touchdowns and 120 receptions for 1,066 yards with two touchdowns. Last season with San Diego, he played in 10 games (two starts) and finished with 59 rushing attempts for 229 yards and one touchdown. Brown also caught eight passes for 88 yards.