The contract is worth $33 million, with $11 million guaranteed, a league source told ESPN.com's Matt Mosley.
The extension was first reported by ESPN NFL Insider Adam Schefter.
Celek's deal runs through the 2016 season. Last week, the Eagles gave right tackle Winston Justice a four-year extension. The team now has 22 players signed through 2012 and beyond.
"It's nice to have basically your core group of guys locked up one way or another and not have to go out into free agency or the draft saying, 'We need this position, We need that position,'" general manager Tom Heckert said. "That's when the mistakes happen. The more guys we can have under contract and obviously the young guys and the guys we expect to be here for a long time, it's the best-case scenario."
Celek has emerged as one of the top players at his position in his first full season as a starter. He's tied for seventh in receptions (54), fifth in yards (601) and tied for fourth in touchdowns (five) among all NFL tight ends. He leads the Eagles in catches and TDs.
"Coming into this season, just like I have every season, I worked [hard] day in and day out," Celek said. "I give it 110 percent every day and that's just the type of guy I am. That's not going to change. I didn't think about a contract situation. I didn't think about anything but winning a Super Bowl. That's our ultimate goal here."
A fifth-round draft choice out of Cincinnati in 2007, Celek has 97 catches for 1,097 yards and seven TDs in 43 career games, including 22 starts.
Celek led Philadelphia with 19 receptions and three TDs in the playoffs last year.
Information from The Associated Press was used in this story.