The Spain international, who won the World Cup with his country this summer, has signed a four-year contract at the Nou Camp after Barcelona agreed a fee in the region of £65million.
The 2024 Ballon d'Or winner leaves City after seven seasons, 298 appearances and 12 major honours, including four Premier League titles, two FA Cups, three EFL Cups and the 2023 Champions League.
"I'm very happy and excited about this new stage in my career. It's a fresh challenge, a chance to experience new things and feel that excitement again," Rodri said.
"I've come to a hugely ambitious club that really suits my personality, so I'll try to help in every way I can to achieve our objectives this season."
The 30-year-old also addressed the prospect of working under Barcelona head coach Hansi Flick, whose methods he expects to differ from those he encountered during his time at Manchester City.
"I'm happy to have a coach who I think will bring a lot to my career," he said. "It's a style that I think is somewhat different from what I've experienced before, so it will be enriching and help me grow as a player."
His final two seasons at the Etihad Stadium were disrupted by injury, but Rodri returned to his best form this summer, being named player of the tournament as Spain won the World Cup for the second time in the nation's history.
In a farewell message to City supporters, Rodri reflected on the life he built in Manchester beyond football.
"I am leaving the club with a huge sense of pride about what we have achieved and gratitude too for so many amazing memories," he said. "What we have done together in these years is something both very special and unforgettable.
"City didn't just make me a 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."
Rodri's exit leaves a significant gap in midfield as City continue a summer of considerable change at the Etihad Stadium under new head coach Enzo Maresca, who succeeded Pep Guardiola this year.