Heckert was named general manager in 2006 after originally joining the team as the director of player personnel in 2001. He spent 10 years in the Miami Dolphins organization before coming to Philadelphia.
"Tom's leadership and work ethic has continued to impress me over the years," said Eagles coach Andy Reid, who also serves as the head of football operations.
Eagles spokesman Derek Boyko said the team had no comment on Licht's departure.
The team also announced the signing of fourth-round draft pick Quintin Demps to a four-year contract on Friday.
Demps, a safety out of UTEP, had 17 interceptions in his career. He picked off five passes last season, returning a pair for touchdowns.
