Patriots coach Bill Belichick announced the move after the NFL draft.
Warren, the third overall pick in the 2001 draft, spent four seasons with Cleveland, two with Denver and three with Oakland, which released him on March 11.
"We've talked with him off and on, and we just were able to work that out," Belichick said. "He's been a very productive player through the course of his career, especially in recent years."
Belichick touched on the versatility of Warren (6-foot-4, 325), who has played a variety of roles at different points of his career. His biggest chance to make an impact in New England figures to be at right defensive end, the spot previously occupied by Richard Seymour and Jarvis Green.
Warren started all 32 games he played in the past two seasons with 57 tackles and six sacks. In his 135 career games, 127 of them starts, he has 229 tackles and 32 sacks. He's reached the playoff just once in nine seasons.
Cleveland drafted Warren three picks before New England took Seymour in 2001. The Patriots traded Seymour to the Raiders before last season. Lewis was taken by St. Louis with the 12th pick in that draft.
Mike Reiss of ESPNBoston.com contributed to this report.