Rodri officially became a City player a day after the La Liga side revealed that the 23-year-old's €70-million (£63 million) release clause had been triggered.
"What City have achieved in the last two years has been amazing and I’m looking forward to being part of such a talented squad," Rodri told the club's official website as part of Thursday's unveiling. "It’s not just the titles they have won, but the way they have managed it, playing attacking football at all times."
The Madrid-born midfielder returned to Atletico from Villarreal last summer for €20 million. Capped six times by Spain, Rodri spent time with Atletico's youth setup before moving to the Yellow Submarine in 2013.
Set to play a pivotal role in City's quest for a third league title on the spin, Rodri will sport the No. 16, last worn by Sergio Aguero when the Argentine striker moved from Atletico in 2011. Aguero switched to the No. 10 shirt in 2015.