Terms of the deal with Adams weren't disclosed.
Adams joined the NFL in 2004 when he signed with the San Francisco 49ers as an undrafted free agent. He made 44 tackles and two interceptions last season with the Browns and also played on special teams.
Browns general manager George Kokinis said Adams "possesses the characteristics we believe in" and praised his versatility.
Adams has big shoes to fill in Cleveland. Jones, a second-round draft pick by the Browns in 2004, had 286 tackles and three forced fumbles in 60 career games and ranked third among safeties behind Baltimore's Ed Reed and St. Louis' Oshiomogho Atogwe with 14 interceptions since 2006.
Copyright 2009 by The Associated Press