Terms were not disclosed but a source told ESPN's Adam Schefter on Sunday that Engram's deal is worth $41.25 million and includes $24 million fully guaranteed.
Engram had received the franchise tag (worth $11.345 million) from the Jaguars earlier this offseason and had until Monday at 4 p.m. ET to agree to a long-term contract.
"Obviously the Jaguars believed in me. They wanted me here as much as I wanted to be here, so I'm blessed and really thankful we got something done. It was up and down. I kind of wish it maybe would have gotten done a little earlier," he told the team's website. "But we got it done. I'm just thankful."
Engram, 28, set career highs in catches (73) and receiving yards (766) to go along with four touchdowns last season. They were the most catches and receiving yards by a tight end in a single season in Jaguars franchise history, surpassing the marks set by Kyle Brady in 2000.
Engram is the fourth tight end in Jaguars franchise history to surpass 50 catches in a season and only the second to surpass 60.
The Giants drafted Engram 23rd overall in 2017, and he caught 262 passes for 2,828 yards and 16 touchdowns in five seasons with New York. He said he wanted a fresh start and felt that signing with the Jaguars last offseason would give him a chance to put up some good numbers in coach Doug Pederson's tight-end-friendly offense.
ESPN's Michael DiRocco contributed to this report.