The 21-year-old England international became the first major close-season signing for City who beat Chelsea 3-2 in the Community Shield season curtain raiser earlier on Sunday.
Everton earlier confirmed the two clubs had agreed a deal.
"Everton have agreed an undisclosed fee with Manchester City for the transfer of Jack Rodwell," the club said on their website (www.evertonfc.com).
"The midfielder is set to undergo a medical with the Premier League champions on Sunday."
Rodwell has been capped twice by England but was not selected for their Euro 2012 campaign after injury.
"I relish the opportunity of playing with some of the best players in the world," Rodwell said on the City website (www.mcfc.co.uk).
"It will be an amazing experience to make my debut in front of them if I am selected to play next weekend."
Rodwell has made 85 appearances for Liverpool-based club Everton, scoring five goals.
City manager Roberto Mancini had recently spoken out about the club's lack of transfer activity.
They have struggled to offload unwanted players such as Roque Santa Cruz and Emmanuel Adebayor while balancing potential new signings with UEFA's financial fair play rules.
Mancini still hopes to bring in more players before the transfer window closes, however.
He said after Sunday's Community Shield win over Chelsea: "We are looking for other players. I don't know which players. I don't want to say which. Speak with Brian Marwood (sporting director)
"I said I was unhappy (on Friday). It is normal. Every manager is unhappy with one week to go and you haven't bought any players.
"I hope we are working and maybe this week or in 10 days we can do something about this. I wait at this moment and tomorrow is the time to talk about new players."
City begin the defence of their Premier League title at home to promoted Southampton on Sunday.
- Jack Rodwell