The Browns surrendered a late-round draft pick, believed to be a seventh-round selection, reports NFL Network's Adam Schefter.
Daniels played in all 16 games last season for Miami, including five starts. He finished with 27 tackles and an interception, playing both cornerback and safety.
The Dolphins took Daniels with a fourth-round draft pick in the 2005 NFL Draft. Then-coach Nick Saban made the pick after coaching Daniels at LSU.
Daniels, entering his fourth NFL season, has played in 44 career games with 25 starts. He started 14 games his rookie season and had 62 tackles and an interception. Daniels recorded 36 tackles and an interception in 2006.
The Associated Press contributed to this report