The Premier League champions announced the signing of the 23-year-old on a five-year deal on Thursday, a day after Atletico announced the 70-million-euro ($79 million £63 million) release clause in his contract had been triggered.
The value of the deal eclipses the reported £60 million City paid Leicester for Algeria international Riyad Mahrez last year.
"I hope this year we get the same or more success as the last two years," said Rodri at joining City, who won a first ever domestic treble of trophies in England last season.
"For me it's a great opportunity. It's a great team with great players in every area of the pitch. I think Pep is the greatest coach in the world and that's what made me come.
"It's important for me. I want to learn and grow as a player. I am very young and have a lot of things to do. With his coaching, I am going grow here."
Rodri's departure will secure a considerable profit for Atletico, who spent 20 million euros last summer to re-sign him from Villarreal after he was released from their youth ranks as a youngster.
He made 47 appearances for Atletico, scoring three goals, as Diego Simeone's men finished above Real Madrid in second in La Liga and won the UEFA Super Cup.
In Rodri, City hope to have finally landed their long-term replacement for the influential Fernandinho.
The Brazilian has been a key member of the squad that has won back-to-back Premier League titles under Guardiola.
However, he is now 34 and struggled with injuries towards the end of last season.
"Rodri has proven himself to be a hugely talented, young midfielder, who has all the attributes we are looking for," said City's director of football Txiki Begiristain.
"He works hard defensively, makes himself available to receive the ball and uses it well when in possession.
"He is a perfect fit for Pep Guardiola's team and we are confident he will be a success."
Rodri's composed style on the ball at the base of the midfield has earned comparisons to Barcelona and Spain midfielder Sergio Busquets, who was handed his debut at the Catalan giants by Guardiola.
"I think he has been the greatest defensive midfielder in last ten years for me, for Barca and Spanish national team," added Rodri.
"I saw him when he started when I was little and I am close to him (in style), but I also have other skills. I am also going to try to learn here from Fernandinho."
Rodri is City's second signing in two days after activating a buy-back clause of £5.3 million to re-sign Spanish left-back Angelino from PSV Eindhoven.