The midfielder sealed a £62.5million switch from Atletico Madrid on Thursday.
He becomes the club’s second most expensive signing behind Kevin De Bruyne, after his deal from Wolfsburg in 2015 reached £68.4m in add-ons.
Rodri will have already delighted the club’s supporters after showcasing his fluent English and intelligence during his first press conference.
The 23-year-old is clearly aware of the significant rivalry with noisy neighbours Manchester United, and he already has a way with words.
“City this last five, six years has changed the story of football not only in Manchester but England,” he said.
“I don’t look for the club, I look for the challenge of the sport. That’s why I moved here.
“I love the City, I love Manchester. I talked to some guys and it is becoming more blue.”
Rodri only spent one season with Atletico, after arriving at the Wanda Metropolitano from Villarreal last summer.
In that time his performances have created optimism that he is the future of Spain’s midfield.
That’s why Man City have not waited around to sign him this summer, triggering his release clause alongside his entourage at La Liga HQ yesterday.
The move will see him work under compatriot Pep Guardiola, yet Rodri insists the former Barcelona and Bayern Munich is not the only reason he chose City.
“I’m not coming here because (Pep) is Spanish,” he added.
“I think he is the greatest coach in the world. That is important for me.
“I want to learn individually and improve as a football player.
“I have a lot of things to do to grow and learn and with this coach I am going to grow here.”
Left-back Angelino also returns to the club after City activated his buy-back clause from PSV Eindhoven.