Roma announced on 1 July (AEST) that the 28-year-old would depart for its Serie A rival, and the transfer has since gone through, with the defender understood to have signed a five-year contract.
Napoli president Aurelio De Laurentiis seemed to confirm the completion of the deal with a "welcome" post on Twitter earlier in the day, before the club followed suit on its official account.
Greece international Manolas spent five years with the Giallorossi after signing from Olympiacos and will bolster Napoli's options at centre-back after the departure of Raul Albiol to Villarreal.
Manolas is Napoli's sixth signing of the close-season, coming after Alex Meret, Giovanni Di Lorenzo, David Ospina, Orestis Karnezis and Luigi Liguori.
The experienced defender will be expected to line up alongside Kalidou Koulibaly, provided the Senegal international does not leave.