Atletico confirm Rodri’s contract at the Wanda Metropolitano has been terminated.
City have paid Rodri’s £62.8m (€70m) release clause.
Atletico Madrid have revealed Rodri will be joining Premier League champions Manchester City.
Rodri was strongly linked with a move to the Etihad in recent weeks and the Citizens have eventually paid the midfielder’s £62.8m (€70m) release clause.
An Atletico statement read: "LaLiga has informed Atletico Madrid that Rodrigo Hernandez, through his lawyer, and representatives from Manchester City, paid the player's release clause at the sports association's headquarters on Wednesday, July 3.
"Manchester City has paid the buyout clause on behalf of the player. The player has therefore unilaterally terminated his contract with our club, which ran until June 30, 2023."
Rodri joined Atletico from Villarreal a year ago, making 47 appearances in all competitions as Diego Simeone's side won the UEFA Super Cup and finished in second spot behind Barcelona in LaLiga.