The 23-year-old is one of City manager Pep Guardiola's main transfer targets, with the club in the market for a successor to their 34-year-old Brazilian defensive midfielder Fernandinho.
"Manchester City has paid the buyout clause on behalf of the player," Atletico said in a statement.
"The player has therefore unilaterally terminated his contract with our club, which ran until June 30, 2023."
Rodri was a member of Atletico's youth team before he joined Villarreal in 2015.
He moved back to Atletico 12 months ago and made 47 appearances in all competitions last season, including 34 in La Liga as Atletico finished runners-up to Barcelona.
Rodri is set to become City's record signing, eclipsing the £60 million (A$107 million) they paid Leicester City to bring Algeria international Riyad Mahrez to the Etihad Stadium in July last year.
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