The 18-year-old winger had spent time training with Maurizio Sarri's side this month after completing a medical ahead of the move.
Ponte have now ratified his departure, reaching an agreement with Napoli over a compensation fee.
"President Vanderlei Pereira and I have been in Italy in person and after lengthy negotiations we have secured the payment which will be paid to Ponte in February," financial director Gustavo Valio told the club's official website.
"Since the player didn't want to play for Ponte anymore and opted for the Italian team, we made every effort to ensure that Ponte's rights were respected and, once the sum is paid, we will withdraw the ongoing judicial action."
Ponte added that his departure for the negotiated fee "proved to be the best solution" following a lengthy legal wrangle over his future.
Leandrinho has scored 11 goals in just 16 appearances for Brazil's Under-17s and finished top scorer as it won the South American U-17 championship in 2015.
His transfer was welcomed by president Aurelio De Laurentiis on Twitter.