After not having been invited to the 2007 NFL Scouting Combine, Celek was drafted by the Philadelphia Eagles in the fifth round (162nd overall) of the 2007 NFL Draft. He signed a four-year contract with the team on May 30, 2007.

In 2008, Celek set franchise records for yards in a game with 131 in week 9 and receptions in a playoff game with 10 in the 2009 NFC Championship game. He caught two touchdowns in a game against the Arizona Cardinals, and his 19 catches during the 2008-09 NFL playoffs were the third most in NFL history for a tight end.

Celek became the starting tight end for the Eagles after L. J. Smith departed via free agency to the Baltimore Ravens in 2009.

Celek signed six-year contract extension on December 1, 2009, to keep him under contract as an Eagle until after the 2016 season.

On December 27, 2009, in week 16 against the Denver Broncos, Celek made four catches for 121 yards and a touchdown, his third 100-yard game of the season. His 47-yard touchdown catch was the longest of his career.

In the 2010 season, Celek caught 42 passes for 511 yards and 4 touchdowns, including a then career-long 65-yard touchdown against the New York Giants in week 15, in the Miracle at the New Meadowlands.

On January 26, 2016, Celek signed a three-year contract extension with the Eagles for $13 million, with $6 million guaranteed.

On March 13, 2018, Celek was released by the Eagles.

On August 31, 2018, Celek announced his retirement from the NFL.

On February 7, 2020, Celek was hired as a personnel consultant in the Eagles’ football operations department, alongside former teammate Darren Sproles.