The move is expected to be finalised in the coming days, bringing to an end seven trophy-laden seasons in Manchester for the 2024 Ballon d'Or winner.
Rodri made 298 appearances for Manchester City after his £62.8m arrival from Atletico Madrid in 2019, a fee that was a club record at the time. He leaves having won 12 major honours, including four Premier League titles, two FA Cups, three EFL Cups and the Champions League in 2022-23.
His final two seasons in England were disrupted by injury, with a serious knee problem sidelining him for much of 2024-25 and a hamstring issue interrupting last season, but he returned to his best form at this summer's World Cup. Rodri led Spain to their second world title and was named player of the tournament, form that appears to have hastened Barcelona's move to complete a deal City had previously resisted.
Manchester City knocked back an opening offer of £38.5m from the Spanish champions last week, with Real Madrid also having been strongly linked as Rodri entered the final year of his contract. Barcelona ultimately stepped up their pursuit in recent days to beat their LaLiga rivals to the signing.
New City boss Enzo Maresca, speaking after Sunday's Community Shield defeat to Arsenal, acknowledged the scale of the challenge posed by losing his captain.
"Rodri is a player who just won the World Cup and Ballon d'Or," Maresca said. "He's a top player, all the teams need a Rodri, so it's not about if we miss Rodri or not."
Rodri's departure would mark the end of an era at the Etihad Stadium, where he established himself as one of the most important midfielders in Pep Guardiola's system before injury disrupted his recent seasons. His arrival at Camp Nou is expected to give Hansi Flick's side further control in midfield as they continue their pursuit of domestic and European honours.
The move continues a busy summer of midfield business for City, who have already broken the British transfer record this window and remain in the market for further reinforcements as they look to reshape the engine room of Guardiola's squad following Rodri's exit.
For Barcelona, meanwhile, landing a player of Rodri's stature represents a statement of intent as they look to build on back-to-back LaLiga titles and mount a fresh challenge for the Champions League.