Umenyiora, 33, played for the New York Giants from 2003 to 2012, winning two Super Bowls with the team and making two Pro Bowls. He spent the last two seasons with the Atlanta Falcons, appearing in 16 games in both and registering a combined 10 sacks.
After Umenyiora's career with the Giants came to an end, he signed a two-year, $8.5 million contract with the Falcons. He made a $2.5 base salary in 2014 with a $4.75 million cap hit.
The Jets have had a busy offseason, headlined by the signing of cornerback Darrelle Revis to a five-year, $70 million deal. Also on defense, the Jets re-signed linebacker Davis Harris to a three-year, $21.5 million deal and added cornerback Buster Skrine and safety Marcus Gilchrist.
Before free agency started, the Jets underwent a front-office makeover by replacing former head coach Rex Ryan with Todd Bowles and former general manager John Idzik with Mike Maccagnan.
- Mike Fiammetta