Terms of the contract are not yet known.
McKinney, a five-year veteran, missed all of last season due to a back injury. Prior to last season, the Texas A&M graduate played in 61 games for the Dolphins, starting 34 of those. While he's listed as a center, McKinney can also play the guard position.
Additionally, the Browns today announced the release of fullback Terrelle Smith, a move that was as unexpected and surprising as a boy-bander outing himself in a national magazine.
Smith was a heralded signing during the 2004 offseason, but the "bruising" blocking back never lived up to his advanced billing. With rookie Lawrence Vickers on the roster and having a much lesser hit against the cap, the eight-year veteran became expendable.
He started 32 of the 48 games he played in Cleveland.