The nine-year veteran logged 33 solo tackles, nine deflected passes, one forced fumble and one fumble recovery for the Dolphins in 2014, his only year with the team.
The Dolphins signed Finnegan to a two-year, $11 million contract in March 2014.
Last season, Miami's defense allowed 5.3 yards per play, which ranked 12th in the league, and 23.3 points per game, which ranked 20th..
The Dolphins finished 8-8 and did not make the playoffs for the sixth straight season.
- Will Green