The Serie A powerhouse have appointed previous Azzurri boss Spalletti to lead the team for the rest of the term.
The experienced coach replaces his predecessor, who was dismissed following the loss to Lazio on Sunday.
Tudor had joined the club in March as Thiago Motta's replacement but left after seven months after an eight-game winless streak.
Under Spalletti, Napoli clinched the Serie A championship in 2022-23 prior to assuming the Italy role, which missed out on the 2022 World Cup during Roberto Mancini's tenure.
Under his guidance, they made it to Euro 2024 but were eliminated in the round of 16 by Switzerland.
Nonetheless, Italy dismissed Spalletti in June after a World Cup qualifying defeat by Norway, as Italy faced the possibility of not making a third World Cup in a row.
He has previously coached Inter Milan, Roma, and Udinese in Italy's top flight and won the Russian Premier League twice with Zenit St Petersburg.
Massimo Brambilla served as interim manager for Juventus during the 3-1 victory over Udinese on Wednesday which left them seventh in Serie A - six points adrift of Napoli at the top after nine rounds.
In the Champions League, they sit 25th in the league phase, with one loss and two draws in their first three games.