Barcelona have agreed to pay City around £65 million, with the 30-year-old set to sign a four-year contract with the LaLiga champions.
"I'm very happy to have arrived. The last few days have been intense, but I'm glad everything has been sorted out. Of course, playing for FC Barcelona is a dream," Rodri told journalists at the airport on Monday.
The Spain international added that he was eager to link up with several familiar faces already at the club.
"I can't wait to be with my team-mates, many of whom I already know from the national team. It's time to get to work and give my very best."
Looking ahead to his first season in Catalonia, Rodri made his ambitions for the club clear.
"The Champions League and everything else that comes our way," he said when asked what he hoped to win with Barcelona.
The 2024 Ballon d'Or winner made 298 appearances across seven trophy-laden seasons at City after joining from Atlético Madrid in 2019 for what was then a club-record £62.8 million. He missed much of the 2024-25 campaign through a serious knee injury, with parts of last season also disrupted by a hamstring issue. Despite those setbacks, Rodri returned to his best at this summer's World Cup, leading Spain to their second title and being named player of the tournament.
He leaves Manchester City having won 12 major honours, including four Premier League titles, two FA Cups, three EFL Cups and the Champions League in 2022-23. City had rejected Barcelona's opening offer of £38.5 million for Rodri, who was entering the final year of his contract at the Etihad.
Real Madrid had also looked to be in the running for his signature before Barcelona stepped up their efforts in recent days to complete the deal.
Rodri's departure leaves a significant void for Manchester City to fill at the base of midfield, with the club having already broken the British transfer record this summer to sign Elliot Anderson from Nottingham Forest and continuing to explore the market for further reinforcements.
His arrival in Catalonia is expected to give Barcelona greater control and tactical flexibility in midfield as they look to build on last season's domestic success and push further in the Champions League.