City triggered the 23-year-old's release clause on Wednesday and deposited the necessary amount at La Liga's headquarters to terminate his contract, the Spanish side confirmed in a statement.
The reigning Premier League champions reportedly paid a club-record €70 million (£62.6 million) for the talented midfielder.
Rodri, who's widely considered the heir to Sergio Busquets in the defensive midfield role, is expected to replace Fernandinho at the base of Pep Guardiola's midfield. Known for his composure and passing range, Rodri is another excellent addition to an already stacked lineup.
Atletico earned a considerable profit on the player, who joined them from Villarreal last year for just €20 million.