McKinney won the starting right guard's job last year and started eight games before he was sidelined by a shoulder injury. He was replaced by Ryan Tucker, who moved over from tackle after serving a four-game suspension.
The 315-pound McKinney has played on both sides of the ball as well as at center during a six-year NFL career.
"With versatility as a guard and center, this signing should solidify the interior part of our offensive line," Browns general manager Phil Savage said in a statement Friday. "At this point, we feel we have seven starters competing for five positions."
McKinney was originally drafted by Miami in the third round in 2002. He played in all 16 games in each of his first three seasons with the Dolphins. He missed the entire '06 season with a neck injury before he signed with the Browns as a free agent before the 2007 season.