Financial terms were not disclosed.
The team is looking for help at the position with Santonio Holmes still recovering from a Lisfranc injury that caused him to miss the majority of last season.
This will be Edwards' third stint with the Jets. The team claimed him off waivers last December after he was cut by the Seattle Seahawks. Edwards previously played with the Jets in 2009 and 2010.
Edwards, 30, caught 18 passes for 199 yards and one touchdown last season. In nine NFL seasons, Edwards has caught 359 passes for 5,522 yards and 40 touchdowns.