The La Liga club announced on Wednesday that City had paid a 70 million euro ($79 million) buyout clause for the tall 23-year-old. City confirmed on their website that Rodri was a record signing.
The deal eclipsed the 60 million pounds they paid Leicester City for Algerian international Riyad Mahrez in July last year.
Rodri -- Rodrigo Hernandez Cascante -- follows Angelino, the Spanish left back who joined from PSV Eindhoven, as manager Pep Guardiola’s second signing of the summer.
"Rodri has proven himself to be a hugely talented, young midfielder, who has all the attributes we are looking for," City's director of football Txiki Begiristain told the City website.
"He works hard defensively, makes himself available to receive the ball and uses it well when in possession. He is a perfect fit for Pep Guardiola’s team and we are confident he will be a success."
City became the first side to claim the English treble of the league championship as well as the FA Cup and League Cup last season.
"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," said Rodri, who has been compared to Barcelona's Spain midfielder Sergio Busquets.
"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."
City said the defensive midfielder, seen as a long-term successor to 34-year-old Brazilian Fernandinho, would play in the number 16 shirt.
The squad number was used by Argentine forward Sergio Aguero, who also joined from Atletico Madrid, from 2011 to 2015 and has been vacant since.
City kick off their 2019-20 Premier League season with a trip to West Ham United on Aug. 10.
(Reporting by Alan Baldwin, editing by Ed Osmond)
