Walton was one of two former Giants' offensive linemen to find a new employer on Thursday. The other was James Brewer, who joined the New York Jets.
Walton started all 16 games for the Giants last season, but his -19.6 Pro Football Focus score was the worst on the offense and his -11.4 run-blocking grade was part of the reason the Giants were 28th in the league with an average of only 3.6 yards per carry.
Walton signed a two-year deal with the Giants, but the team cut him after the first season. Weston Richburg is expected to the team's starting center in 2015.
In Miami, Walton is likely to back up starting center Mike Pouncey.
Be sure to check our Giants Free Agency Tracker for the latest news and rumors