City triggered the buy-out clause in the 23-year-old's Atleti contract after convincing him to move to the Etihad Stadium.
The Spain international has signed a five-year deal with the Premier League champions.
“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, who will wear the No. 16 shirt, told City’s official website.
“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.”
Txiki Begiristain, City’s director of football 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.
“He is a perfect fit for Pep Guardiola’s team and we are confident he will be a success.”
City identified Rodri as their No.1 target for the deep-lying midfield role towards the end of last season, and had been confident of wrapping up his signature as far back as April.
The midfielder had second thoughts about his future in June as Atleti made efforts to sign him to a new contract, while Bayern Munich also made a serious attempt to bring him to Bavaria.
But the prospect of working with Pep Guardiola played a key part in his decision making, and the two men talked at length just before Rodri communicated his decision to Atleti boss Diego Simeone.
The capture of Rodri brings City's long and troubled search for a defensive midfielder to an end.
The Blues failed in their attempt to sign Fred from Shakhtar Donetsk in January 2018, before a move for Jorginho fell through despite agreeing personal terms with the player and a transfer fee with Napoli. The Italian club later refused to sell to City, insisting he go to Chelsea as part of the deal that took Maurizio Sarri to Stamford Bridge.
But sources close to Guardiola's coaching staff insist they are delighted to get their hands on Rodri, who has long been seen as Spain's successor to Barcelona lynchpin Sergio Busquets.