Guyton started 32 games for the Patriots and has career totals of 4½ sacks, three interceptions and three fumble recoveries.
He signed with New England as an undrafted free agent in 2008. The Dolphins confirmed their deal with him Tuesday.
The Dolphins also added veteran receiver Legedu Naanee. He signed a one-year contract, his agent, David Canter, said. ESPN NFL Insider Adam Schefter initially reported the signing.
Last year with Carolina, Naanee started 10 games and had 44 catches for 467 yards, all career highs. He spent his first four NFL seasons with San Diego and has 107 career receptions.
Information from The Associated Press was used in this report.