The 26-year-old Cameroon international played 30 times for Napoli on loan as they finished third in Serie A this season.
Anguissa joined the Cottagers from Marseille in 2018 and made 66 appearances for the west London club.
He spent the 2019-20 season on loan with Villarreal before returning to Craven Cottage the following season.
Fulham were relegated from the Premier League in both seasons he played with the cub.
He joins Napoli for an undisclosed fee after the club exercised their option to make his deal permanent.
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