Manchester City have paid Rodri's £62.8m (€70m) release clause, Atletico Madrid have confirmed, with his move to the Etihad now a formality.
The Premier League champions deposited the sum at La Liga's headquarters on Wednesday.
The Citizens will make the Spain international their most expensive player in their history, topping Riyad Mahrez, who cost £60m from Leicester last year.
A statement from the Spanish club read: "Manchester City pays Rodrigo's buyout clause at LaLiga headquarters.
"The player has unilaterally terminated his contract with our club."
Pep Guardiola acquires the 23-year-old, whose full name is Rodrigo Hernandez, to bolster his midfield options.
Despite edging Liverpool to the league title, City's failure to break through in the Champions League left some disappointment.
But with Rodri's arrival, City appear primed to challenge strongly for Europe's top honour in club football.
Atletico had already reallocated Rodri's No 14 jersey to his replacement, Marcos Llorente, who signed for £36m from Real Madrid.
