Arsenal and Chelsea both missed out on the 32-year-old, whose City contract expired at the end of June.
"I have a lot of emotions. I am very happy and proud, and excited to start this new chapter and this new journey," Stones told Inter's official channel.
The move ends a decade at City that yielded six Premier League titles, the Champions League, two FA Cups, five League Cups, three Community Shields, the Club World Cup and the Uefa Super Cup.
"I've lived all my dreams out," Stones said of his time at the Etihad Stadium. He becomes the second former City defender to move to San Siro this year, following Manuel Akanji's loan switch being made permanent earlier in the summer.
Stones' path to Manchester City began at Barnsley and continued through Everton, from where City paid £47.5m to sign him in 2016 — a fee that briefly made him one of the most expensive defenders on the planet. What followed was 295 appearances and 19 goals in sky blue, built on a passing range and composure that made him a favourite of Pep Guardiola's build-up play, though his final campaigns were increasingly interrupted by injury; he made just nine Premier League starts last season as Ruben Dias and Nathan Ake took on greater shares of the workload.
Internationally, his 93rd cap came this summer as part of England's run to a World Cup semi-final, a tournament in which he started the quarter-final defeat of Norway before the Three Lions fell 2-1 to Argentina at the last-four stage, finishing third overall.
Inter Milan, who begin their Serie A title defence at home to newly promoted Monza on August 22 after winning a 21st league championship last season, described the move as the start of a "new chapter" for Stones after "32 years in England." Reports in Italy have suggested the deal is worth around €4 million a season.
The move continues a summer in which several of England's World Cup contingent have opted to test themselves outside the Premier League, following Jude Bellingham and Harry Kane's earlier moves to Real Madrid and Bayern Munich.
For Inter, adding a defender with Stones' medal collection and ball-playing profile is a clear statement of intent as they look to build on last season's title and push further in Europe.