On Wednesday, Omar Berrada, City’s chief operating officer, was pictured arriving at the LaLiga headquarters in Madrid to complete the deal.
The 23-year-old midfielder has signed a five-year deal, the Premier League club announced.
Rodri officially became a City player the day after the LaLiga outfit revealed the €70m – around £62.8m – release clause in his contract, which had four years to run, had been triggered.
A statement on the reigning champions’ official website said: “Manchester City are delighted to announce the signing of Spanish midfielder Rodri.
“The 23-year-old joins on a five-year deal from Atletico Madrid and follows Angelino to become Pep Guardiola’s second signing of the summer.”
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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.
“I can’t wait to start working with Pep Guardiola and my new team-mates, and hopefully we can achieve great things together.The deal for the holding midfielder will be a club record sum, surpassing the £60million paid for Riyad Mahrez last summer.
The 23-year-old is Man City’s second signing of the summer, with left-back Angelino completing his £5million return to the club on Wednesday.
Angelino, the Spain Under-21s international, played every game for PSV last season as they were pipped to the Eredivisie title by Ajax.
Several clubs, including Arsenal, were monitoring the progress of the defender but would have had to pay at least £20million for his services.
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