The Premier League champions announced his capture via Twitter on Thursday:
Per John Edwards for the club's website, 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."
City confirmed in their announcement that Rodri, who had a £62.8 million buyout clause, is the club's record signing. He has surpassed their previous £60 million recordset by Riyad Mahrez's arrival from Leicester City last year.
Having spent six years with Atleti in his youth, the 23-year-old returned to Los Rojiblancos in 2018 after beginning his senior career at Villarreal.
He made 47 appearances in all competitions as Atletico finished second in La Liga and went out of the UEFA Champions League in the round of 16.
Goal provided a profile of the defensive midfielder:
As Samuel Luckhurst of the Manchester Evening News observed, City now have an incredible array of high-level options to call upon in midfield:
Rodri will have primarily been brought in as a long-term successor to Fernandinho, who turned 34 in May.
The Spaniard is a robust ball-winner in midfield whose physicality and 6'3" frame should make him well-suited to the rigours of Premier League football, and he'll add protection to City's back line.
He's excellent on the ball, too, as you would expect from a Pep Guardiola midfielder, so he should equally have little trouble adapting to the coach's demands when in possession.
Fernandinho has one more year remaining on his contract at City, and by the time that deal comes to an end Rodri should be settled and ready to take on the Brazilian's responsibilities fully.