The 23-year-old Hojlund scored 16 goals in 44 appearances across all competitions last season, helping Napoli win the Supercoppa Italiana and finish runners-up in Serie A.
The forward joined United from Atalanta in 2023 and went on to score 26 goals in 95 appearances for the Premier League club.
He was also part of the United squad that lifted the FA Cup in May 2024, coming on as a substitute in the final against Manchester City at Wembley.
Hojlund returned to Italy at the start of the 2025-26 campaign on a season-long loan.
"Everyone at the club would like to wish Rasmus all the very best for the future," United said in a statement.
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