The 28-year-old Serbian international has been with Torino since 2020, making 158 appearances across all competitions.
"Napoli announces that they have secured Vanja Milinkovic-Savic on loan from Torino with an option to buy," the club stated in an announcement on Saturday evening.
The Serbian will compete with Napoli's starting goalkeeper, Italian Alex Meret, who is also 28.
Napoli has been the most proactive Italian club this summer, signing eight players, including Kevin De Bruyne, whose contract with Manchester City has lapsed, and Dutchman Sam Beukema, who was acquired from Bologna for 31 million euros.
Napoli is still aiming to transfer Victor Osimhen to Galatasaray, but talks with the Turkish club, where the Nigerian striker was on loan last season, are still stalled over the transfer fee, which the Italians have set at 75 million euros.
The 2025/26 Serie A season will commence on 23 August.