He was among four players claimed by the Jets on Sunday. New York also claimed wide receivers Kalif Raymond (from the Denver Broncos), Damore'ea Stringfellow (from the Miami Dolphins) and linebacker Edmond Robinson (from the Minnesota Vikings).
Tye, 25, was released Saturday after two seasons with the New York Giants. He started 10 games and caught 48 passes for 395 yards and a touchdown last season, but he fell down the depth chart after the Giants added free agent Rhett Ellison and No. 1 pick Evan Engram.
The Jets are thin at tight end because presumptive starter Austin Seferian-Jenkins is serving a two-game suspension stemming from a DUI arrest last September.