The terms of the deal were not revealed on Thursday, but reports last month suggested the defender was set to join on an initial loan with an obligation to buy.
Serie A officially listed the transfer as a loan on its website on Wednesday.
Bellanova had joined Cagliari permanently in May following a similar agreement with Bordeaux, his prior parent club.
The 22-year-old Italy youth international stood out in Serie A last season, scoring one goal and assisting two more in 31 games. He created 32 chances – the 13th-most among all defenders.
However, Bellanova could not rescue Cagliari from relegation, as they finished a point behind Salernitana in 18th place.
He becomes the fifth new recruit for the 2022-23 season, joining Andre Onana, Henrikh Mkhitaryan, the returning Romelu Lukaku and Kristjan Asllani at Inter.
The Nerazzurri have also made loan moves for Robin Gosens and Joaquin Correa permanent.