Godin, who announced in May that he would leave Atleti at the end of the season, made 389 appearances in nine years with the club, having arrived from Villarreal in 2010.
During that time, the 33-year-old won the 2013-14 La Liga title and two Europa League crowns, as well as the Copa del Rey, Supercopa de Espana and a trio of UEFA Super Cups.
Godin also played in two Champions League finals, losing to Real Madrid on both occasions.
The former Atleti captain, who has won 131 caps for his country, was widely expected to join Inter after revealing he would depart the Wanda Metropolitano.
“FC Internazionale Milano announces that a contract has been agreed with Diego Godin that will run until 30 June 2022,” read an Inter statement.
Godin becomes the second major signing of Antonio Conte’s Inter reign, after the club exercised an option to buy Sassuolo winger Matteo Politano, who spent last season on loan at San Siro.
Provided by Press Association Sport
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