Petty spent three seasons with New York after being selected in the fourth round of the 2015 draft. He played in 10 games for the Jets, throwing for 1,353 yards and four touchdowns with 10 interceptions, and went 1-6 as a starter.
Tannehill has suffered two major left knee injuries in the past 18 months and missed all of last season, but he is expected to be ready for offseason drills.
The Dolphins didn’t take a quarterback in the draft. The Jets selected USC quarterback Sam Darnold with the No. 3 overall pick.