Hill, 28, has been a valuable blocker, pass-catcher and special-teams player for the Saints since they first signed him as an undrafted free agent from Idaho State in 2013. He is one of only six players on the roster who have been with the Saints for more than four years.
The 6-foot-5, 250-pounder has 16 catches for 185 yards and a touchdown this year. He has 83 catches for 799 yards and 11 TDs during his six-year career.
"He's been invaluable for us because he literally does so many jobs. He's a complete tight end," Saints tight ends coach Dan Campbell told NOLA.com last week. "We ask him to do a ton, from blocking to pass protection. We ask him to pass protect one on one with defensive ends, and then we ask him to block the point of attack with a D-end. And then we'll ask him to run the seam, or we'll throw him a screen pass.
"His job description every week, it's like we give him the details to the game plan and it could be anything, and he's ready for that. And he's done a hell of a job."
Hill's deal includes a $3 million signing bonus.