Hojliund joined the Serie A side on loan last summer with an obligation to buy for €44 million (£38m) after struggling during his two years at Old Trafford.
Napoli have since triggered the conditions to sign him permanently from Man United after they secured Champions League football.
According to Nicolo Schira, the 23-year-old has signed a four-year deal in Naples until 2030, and there is also an €85m release clause in his contract that is valid from July 2027.
Hojlund has found a new lease of life since moving to Italy, surpassing the 15-goal mark in all competitions after scoring in added time of Napoli's 3-0 victory over Pisa on Sunday.
United will also be pleased that a deal has finally been agreed, so they can move on from Denmark international, even if they've recorded a £34m loss by offloading him.