Rodri, 23, officially became a City player a day after the La Liga club revealed the 70-million-euro (£63 million) release clause in his contract had been triggered.
Man City sign Spain international Rodri for club record fee
Premier League champions Manchester City on Thursday announced the signing of Spain midfielder Rodri on a five-year deal from Atletico Madrid for a club record fee.
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"Manchester City are delighted to announce the signing of Spanish midfielder Rodri," said a statement on the club's website.
The value of the release clause eclipses the reported £60 million City paid Leicester for Algeria international Riyad Mahrez last year.
Rodri said: "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.
"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."
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