The move will save the Dolphins $5 million in cap space.
Sitton is likely to wind up with the New York Jets, a source tells ESPN's Adam Schefter. There he would reunite with Jets coach Adam Gase, formerly of the Dolphins.
Sitton, 32, signed a two-year, $13.5 million deal with the Dolphins last March with hopes of fortifying Miami's interior offensive line. Sitton's season ended shortly after it started when he tore his rotator cuff in Week 1 versus Tennessee.
Sitton had surgery and was placed on injured reserve in September.
The 6-foot-3, 320-pound veteran guard is a four-time Pro Bowler who has played 11 NFL seasons, including his first eight in Green Bay.
The Dolphins will now have to find at least two new starters, and possibly more, on their offensive line. Right tackle Ja'Wuan James departed in free agency, landing a four-year, $51 million deal with the Denver Broncos.