Vannett signed with the Giants' practice squad Tuesday, Art Stapleton of The Bergen Record reports.
Vannett was waived by the Saints on Saturday and will now get a chance to make an impact in New York. The veteran tight end spent most the season as a healthy scratch and failed to carve out a consistent role in New Orleans. He did however find his way onto the active roster for four games, making two catches for 13 yards on two targets.