The team announced the deal on Friday.
The 6-foot-1, 317-pound Franklin started nine games for the Saints last season and recorded 17 tackles. He has 204 career tackles.
The Chargers also agreed on a one-year contract Friday with running back Jackie Battle.
The 6-2, 238-pound Battle, who is a special teams standout, rushed for 597 yards and two touchdowns while adding nine receptions for 68 yards while playing for Kansas City last season.
The Chargers also released rookie free agent fullback Mohamed Marah.