The Spain midfielder has been highly impressive in the Spanish capital since moving fromVillarreallast summer.
He has won his place in the national team set-up due to his performances and now Atleti will receive a sum of €70m, considerably higher than the €25m they paid for him a year ago.
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“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 is the English champions’ first major acquisition of the summer, with American goalkeeper Zach Steffen’s summer move having been confirmed midway through last season.