Henry, 26, clicked with rookie quarterback Justin Herbert and had a career-best 60 receptions for 613 yards and four touchdowns for the Chargers last season.
He will join a Patriots team that is undergoing a pass-catching overhaul. On Monday, the team agreed to a total of nearly $100 million worth of contracts to tight end Jonnu Smith and wide receivers Nelson Agholor and Kendrick Bourne.
Patriots coach Bill Belichick has long favored a two-tight-end approach, having used first-round picks at the position in 2002 (Daniel Graham) and 2004 (Benjamin Watson) and later pairing Rob Gronkowski and Aaron Hernandez together in his second decade as Patriots coach.
Now he'll have Henry with Smith to help address a position that has been somewhat of a nonfactor since Gronkowski's departure in 2018. No other team in the NFL has had lower pass-catching production from tight ends over the past two seasons.
Henry (6-foot-5, 250 pounds) played last season on the franchise tender, making $10.6 million.
He has yet to play a full season in his NFL career and missed the final two games last season after being placed on the reserve/COVID-19 list. He missed the entire 2018 regular season after tearing an ACL and four games in 2019 after suffering a tibial plateau fracture in an opening-week victory over the Indianapolis Colts.
Selected by the Chargers in the second round of the 2016 draft, Henry has 196 receptions for 2,322 yards and 21 touchdowns in five NFL seasons.
Belichick has long admired Henry, saying in December that he has followed his career since Henry was at Pulaski Academy in Little Rock, Arkansas, under innovative high school coach Kevin Kelley.
ESPN's Mike Reiss and Shelley Smith contributed to this report.