The Brazilian defender's departure, already expected, follows that of Eljif Elmas, whose loan from RB Leipzig was not made permanent.
Juan Jesus was central to Antonio Conte's plans during his time at the club, but there is no room for him under new head coach Massimiliano Allegri.
Napoli confirmed the exit with a warm farewell message.
"The SSC Napoli thanks and bids farewell to Juan Jesus, whose contract with the club has come to an end. In the blue shirt since August 2021, Juan played 130 matches for Napoli, scoring five goals. He contributed to winning two Scudetti and the Italian Super Cup last 22 December.
"Juan Jesus has our most sincere thanks for the professionalism, the spirit of sacrifice and the attachment to the shirt he showed throughout his time at Napoli. The club wishes him all the best for the future and every success for the rest of his career."
The 35-year-old defender leaves with 142 appearances and one goal for Inter, 130 appearances and five goals for Napoli, 102 appearances and one goal for Roma, and 42 matches for Internacional across his career.
He also won four caps for Brazil's senior side, six with the Olympic team and 13 at Under-20 level, and his honours include two Serie A titles, an Italian Super Cup, a Copa Libertadores, a Campeonato Gaucho, a Recopa Sudamericana and both the Under-20 World Cup and South American Under-20 title.
Attention at Napoli is now firmly on his replacement. The club continue to push for Lazio centre-back Mario Gila, considered one of the ideal profiles to strengthen the back line ahead of next season, according to Sky Sport.
The Spanish defender is among the leading targets for the new Allegri era, and Napoli want to get the deal done before any rivals can move in.
Sporting director Giovanni Manna held a further meeting with the entourage of the 2002-born centre-back in recent hours, underlining Napoli's determination to keep a privileged position in the talks.
Parallel discussions with Lazio remain ongoing, with both clubs working towards an agreement that satisfies each side.
Napoli's aim is to hand Allegri one of the first reinforcements of his new cycle in defence, and confidence inside the club remains high that contacts in the coming days can produce a breakthrough.