The Spanish midfielder joins City on a five-year deal after they activated his release clause at the Wanda Metropolitano.
The cost of the deal for the 23-year-old who has been earmarked as a long-term replacement for Fernandinho makes him the most expensive signing in City’s history.
‘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,’ he 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.’
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