New York brought on Cooter as the team's next running backs coach.
Cooter previously ran the Detroit Lions' offense in the last three seasons. Detroit parted ways with him in January after the offense regressed under first-year head coach Matt Patricia.
Cooter will work under new head coach Adam Gase and offensive coordinator/quarterbacks coach Dowell Loggains. He has never been a running backs coach, but worked with Gase on the Denver Broncos' coaching staff in 2013.
Cooter was a Broncos offensive assistant when Gase held the offensive coordinator job.
Detroit's offense averaged 327.2 yards per game last season, which ranked 24th in the NFL. The Lions ranked 25th in the league with 20.2 points per game.
The Jets also announced the additions of Shawn Jefferson as assistant head coach offense/wide receivers, Bo Hardegree as an offensive assistant, John Dunn as tight ends coach, Frank Pollack as offensive line coach, Derek Frazier as assistant offensive line coach, Frank Bush as assistant head coach defense/inside linebackers, Andre Carter as defensive line coach, Joe Vitt as senior defensive assistant/outside linebackers, Blake Williams as a defensive assistant and Eric Sanders as a defensive assistant.