The Ballon d'Or winner had been in talks with Real Madrid for several weeks, but negotiations slowed down, giving Barcelona the chance to make their move before the new La Liga season.
Rodri's agent, Pablo Barquero, confirmed that the midfielder has chosen Barcelona despite strong interest from their biggest rivals.
Barquero said: "Out of respect for Madrid, as they have been class, Rodri informed them that his decision is to join Barca."
He also confirmed that Rodri's personal terms with Barcelona have been fully agreed.
Rodri remains under contract with Manchester City until June 30, 2027, meaning Barcelona will still have to agree a transfer fee with the Premier League club before the move can be completed.
Barcelona's push to sign the midfielder gathered momentum after Rodri held talks with manager Hansi Flick and sporting director Deco. Those discussions are believed to have played a key role in convincing the Spain international to move to Camp Nou.
The transfer would be a major boost for Barcelona as they look to strengthen their squad with one of the world's best midfielders ahead of the new campaign.
Real Madrid, meanwhile, will now have to turn their attention to other targets after missing out on the Manchester City star. Jose Mourinho's side have already added Marc Cucurella, Bernardo Silva, Ibrahima Konate, Denzel Dumfries, Carlos Espi and Yan Diomande during the transfer window.
With Rodri now set on joining Barcelona, Real Madrid will look to complete any remaining business before they begin their La Liga season against Espanyol on August 22.
Atletico Madrid have reportedly moved into pole position to sign Tottenham Hotspur captain Cristian Romero as the Spanish club push to complete a deal before the European summer transfer window closes.
Chelsea defender Tosin Adarabioyo believes new signings Jordan Henderson and Danny Welbeck will add valuable experience to the squad, while praising Mykhailo Mudryk's work rate as the winger continues his return to action.
Paris Saint-Germain have completed the signing of France midfielder Maghnes Akliouche from Monaco in a deal worth close to 50 million euros, with the 24-year-old committing his future to the European champions until 2031.
Bournemouth have completed the signing of Spanish right-back Juanlu Sanchez from Sevilla in a deal reported to be worth 11.2 million pounds.
