Manchester City have signed Rodri from Atletico Madrid for €70 million, making him the most expensive signing in their history.
City had made the central midfielder one of their top transfer targets this summer but, according to ESPN FC sources, faced competition from Bayern Munich.
"What City have achieved in the last two years has been amazing and I'm looking forward to being part of such a talented squad," Rodri said. "It's not just the titles they have won, but the way they have managed it, playing attacking football at all times.
"It's a style that excites me, as do the club's ambitions. I can't wait to start working with Pep Guardiola and my new team-mates and hopefully we can achieve great things together."
City director Txiki Begiristain added: "Rodri has proven himself to be a hugely talented, young midfielder, who has all the attributes we are looking for.
"He works hard defensively, makes himself available to receive the ball and uses it well when in possession."
Rodri moved to the Wanda Metropolitano from Villarreal last summer for an up front payment of €20m and the Rojiblancos have made a significant profit on their original outlay.
City's previous most expensive signing was Riyad Mahrez, who joined from Leicester for £60m last summer.