Another former New York Jet has followed coach Eric Mangini to Cleveland.
Terms of the deal weren't disclosed.
"David is another example of the emphasis that we place on toughness, leadership and versatility," Browns general manager George Kokinis said in a statement released by the team. "He has played inside and outside linebacker and has been a core special-teams player throughout his career."
Bowens started five of 16 games for the Jets in 2008, registering 40 tackles, four sacks, two forced fumbles and an interception. He also added nine special-teams tackles.
Bowens, 31, originally was a fifth-round draft pick of the Denver Broncos in 1999. In addition to his two-year stint with the Jets, he has played with the Broncos (1999), Green Bay Packers (2000), Washington Redskins (2001) and Miami Dolphins (2001-2006).
Also on Thursday, the Browns released offensive tackle Kevin Shaffer, who had started 47 games in three seasons with the team. Shaffer, 29, started his NFL career in 2002 with the Atlanta Falcons and spent four seasons with the team, becoming a regular starter in 2004 and 2005.