Silver noted Celek will make it official with a statement on the Eagles' website Friday morning.
The 33-year-old Cincinnati native had urged his teammates to realize the rarity of getting into championship contention during the team's postseason run.
"Everybody in this locker room understands, these opportunities don't come. This could be all our shot," he told reporters in January. "For me especially, getting older...you know. This is a big opportunity. We can't take it lightly."
Celek spent his entire career in Philly after the organization selected him in the fifth round of the 2007 NFL draft from the University of Cincinnati.
His best statistical season came in 2009 when he posted career highs in receptions (76), receiving yards (971) and touchdowns (eight).
The emergence of fellow tight end Zach Ertz caused his impact to diminish in recent years, though. He tallied just 27 catches and one score over the past two seasons combined. Pro Football Focus graded him as the league's No. 65 tight end in 2017.
In all, Celek tallied 398 grabs for 4,998 yards and 31 TDs across 175 regular-season appearances. He only missed one game as a pro, which came in 2012 when a concussion sidelined him.
Along with his on-field impact, the tight end also created the Take Flight Foundation, which works to "provide seriously ill and physically challenged children throughout Greater Philadelphia with daily support and life-changing experiences."