The Rams announced the deal Tuesday for Matthews, the former USC star who spent the past decade with the Packers.
Matthews had 83 sacks in his 10 seasons with the Packers, earning six Pro Bowl selections and winning a Super Bowl ring. He has been a standout pass-rusher throughout his career, although his 3 sacks last season were the lowest total of his decade in the NFL.
Matthews is a native of Agoura Hills, California, who lives in nearby Calabasas. Both towns are near the Rams' training complex in Thousand Oaks.
Matthews also played four seasons for the Trojans at the Coliseum.