Henry is expected to earn more than $11 million in 2020, based on the projected 2020 salary-cap figure.
Chargers general manager Tom Telesco said last month at the NFL scouting combine that tagging Henry was a possibility, given the team's desire to retain him.
A second-round pick in 2016 from Arkansas, Henry has established himself as a promising tight end to replace future Hall of Famer Antonio Gates, despite missing the entire 2018 season because of a knee injury suffered during offseason activities.
Henry, 25, has caught 136 passes for 1,709 yards and 17 touchdowns in three seasons. Last season, he set single-season career highs with 55 receptions and 652 receiving yards.
Following a 5-11 season, the Chargers have been active this offseason in retooling their roster.
In a deal that will not be official until the start of the new league year on March 18, the Chargers traded left tackle Russell Okung to the Carolina Panthers for guard Trai Turner. They also have signed running back Austin Ekeler to a new, four-year, $24.5 million contract.