Quinn, 36, spent the last two years on coach Nick Saban's staff with the Dolphins. He had one year remaining on his contract with Miami, but according to reports, was dismissed by new coach Cam Cameron when he declined to sign a new, two-year contract.
It is believed Quinn's deal with the Jets is for two seasons. He was contacted by several NFL teams after the Dolphins fired him and interviewed with New York officials late last week.
In Quinn's two seasons with the Dolphins, the defense statistically finished No. 18 and No. 4 in total defense and averaged 48 sacks a season. And that was working with one of the oldest lines in the NFL.
With the Jets, Quinn, known as an excellent teacher, will work with a much younger line as the Jets in 2007 move into the second season of their transition to a 3-4 front.
Quinn will replace longtime defensive line coach Denny Marcin, who is expected to retire or be reassigned within the organization.
A college defensive lineman at Division III Salisbury State (1990-93), Quinn coach six seasons at the college level before joining the San Francisco 49ers staff in 2001. He was then hired by Saban in 2004.
Len Pasquarelli is a senior NFL writer for ESPN.com.