The deal reportedly is worth $20 million.
Cox, 26, had four picks in 12 games last year. He's expected to slide into the starting lineup. Both of San Diego's starting cornerbacks, Quentin Jammer and Antoine Cason, are expected to leave as unrestricted free agents.
Rinehart's signing came a day after former Philadelphia Eagles tackle King Dunlap agreed to a two-year contract and former Dallas Cowboys tight end John Phillips agreed to a three-year contract. Dunlap and Phillips signed their deals Tuesday.
Rinehart is being reunited with his former position coaches in Buffalo, Joe D'Alessandris and Andrew Dees. Rinehart was limited to seven games and two starts at right guard in 2012 due to an ankle injury that landed him on injured reserve on Nov. 2.
Rinehart's agent, Leo Goeas, was a Chargers tackle from 1990-92.
Also Wednesday, wide receiver-returner Richard Goodman signed his one-year tender as an exclusive-rights free agent.