The 21-year-old has signed for a fee of £12m, which could rise to £17m.
Rodwell completed a medical with the Premier League champions on Sunday before signing a deal to become Roberto Mancini's first signing of the summer.
"I relish the opportunity of playing with some of the best players in the world and continuing my development," said Rodwell.
"It will be an amazing experience to make my debut in front of them if I am selected to play next weekend.
"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."
Despite having all the attributes required to play at the top of the game, we still don't know exactly how good Jack Rodwell could become as his injury problems at Everton have stopped him ever stringing together 15-20 games in a row. I'm concerned, however, that he is making the same mistake made by so many English youngsters. His words say it all - "... IF I'm selected ...".
Scott Parker, Shaun Wright-Phillips and Joe Cole (to be followed by Adam Johnson and James Milner) all made big moves too early and failed to get enough football in their early twenties, which undoubted affected their ability to live up to their potential.
Don't get me wrong, I attach no blame to Rodwell for his decision to move to a team set to dominate English football for the foreseeable future (nor Everton for taking the money) and this move could be the making of him, but as an England fan I've seen this all before and it rarely ends well.
Prove me wrong Jack.