He played college football for the Ole Miss Rebels, earning first-team All-American honors in 2016.

A 3–star tight end recruit, Engram committed to play college football at Ole Miss over offers from Georgia State, Marshall, South Alabama, Toledo, and Wake Forest, among others.

[4][5] In his last year at Ole Miss, on 65 receptions, Engram netted 926 yards and eight touchdowns, a performance that earned him the Conerly Trophy.

[14] Engram was selected to upgrade a Giants tight end core that only had three touchdown receptions the previous year.

[16] Throughout training camp, he was slated to take the vacant starting tight end role that used to belong to Larry Donnell.

[18] On September 18, 2017, Engram caught four passes for 49 yards and a touchdown in a 24–10 loss to the Detroit Lions on Monday Night Football.

[19] On December 3, 2017, Engram caught seven passes for a season-high 99 receiving yards and a touchdown during a 24–17 loss at the Oakland Raiders.

Head coach Ben McAdoo was fired after the game due to the Giants posting a 2–10 record.

In Week 15, he made a season-high eight receptions for 87 yards and had his first carry of his career for a 14-yard gain as the Giants lost 34–29 to the Philadelphia Eagles.

[25][26] Engram recorded his first career 100-yard game in a Week 1 35–17 loss to the Cowboys with 11 receptions, 116 yards, and a touchdown.

[30] On April 29, 2020, the Giants picked up the fifth-year option on Engram's contract.,[31] worth $6.013 million fully guaranteed for the 2021 season.

[42] In Week 8, Engram scored his first touchdown as a Jacksonville Jaguar in a 21–17 loss to the Denver Broncos.

[53] Engram was ruled out for the season on December 13, 2024, after suffering a torn labrum during Jacksonville's Week 14 game against the Tennessee Titans.