Rodwell has signed a five year-deal to leave Goodison Park to join the Premier League champions for an undisclosed fee.
The 21-year-old told City's official website: "I relish the opportunity of playing with some of the best players in the world and continuing my development.
"I look forward to working with Mr. Mancini and his coaching staff and ultimately playing in front of the City fans at the Etihad Stadium.
"The hard work starts today as I start to help contribute to the club winning more silverware. The season has started really well with the Community Shield win."
The midfielder will join up with Roy Hodgson's England squad to play Italy this week before going into contention to make his City debut against Southampton on Sunday, August 20.