The midfielder, who was named player of the tournament as he captained Spain to World Cup glory this summer, put pen to paper on a four-year contract with the Catalan giants on Tuesday.
"I'm very happy and excited about this new stage in my career," the 30-year-old said. "It's a fresh challenge, a chance to experience new things and feel that excitement again.
"I'm here to compete for everything, for big things like the Champions League. I've come to a hugely ambitious club that really suits my personality, so I'll try to help in every way I can."
Rodri, who joined from Atletico Madrid in July 2019 when City paid a then club-record Stg 62.6m ($A119.1 m), had entered into the final year of his contract at the Etihad Stadium.
Barcelona saw an initial £40m ($A76 m) offer and an increased bid turned down before an agreement was struck on Sunday, despite new City boss Enzo Maresca admitting he wanted to keep the 2024 Ballon d'Or winner.
Rodri helped City win four Premier League titles, two FA Cups and three League Cups, while he scored the only goal when they edged out Inter Milan in the 2023 Champions League final.
However, an anterior cruciate ligament injury in the 2024-25 season and hamstring and groin problems in the 2025-26 season – Pep Guardiola's last at the club – have restricted his involvement.
Now, he links up with several familiar faces as Spain teammates Lamine Yamal, Dani Olmo, Pedri, Gavi, Pau Cubarsi and Eric Garcia and Joan Garcia are at Barcelona.
"I'm joining a dressing room that I know perfectly well, so that will help me settle in. What I'm worried about are the jokes in the first few days," a smiling Rodri added.
Rodri flew to Barcelona's El Prat airport on Monday ahead of the deal being finalised following a medical and told reporters: "Playing for Barcelona is a dream come true for me."
In a message to City fans on the club's official website, he wrote: "City didn't just make me grow as a player. They made me grow as a human. I saw my brother graduating from Manchester Metropolitan University. I could see my girlfriend working for the NHS.
"Manchester shaped my whole life. It's time to say goodbye, thanks to the club, the fans, the staff and my team-mates. This journey couldn't be the same without you, my heart will always be blue."
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