The experienced Uruguayan centre-back spent just a single season with Antonio Conte's men before being deemed surplus to requirements.
Cagliari confirmed Godin – who won two Europa League titles and one LaLiga crown during his time with Atletico Madrid – has signed a three-year contract, meaning he will be tied to the club until he is 37.
Godin made 23 Serie A appearances as Inter finished second to Juventus last term, while he also helped them reach the Europa League final, scoring as the Nerazzurri were beaten 3-2 by Sevilla.
Cagliari, who finished 14th in Serie A last term, already have a strong contingent of Uruguayans, with Gaston Pereiro, Nahitan Nandez and Christian Oliva at the club.
It began its 2020-2021 campaign with a 1-1 draw at Sassuolo.