Rodwell signed a five-year contract at the Etihad on Sunday, ending an association with the Toffees that started at the age of seven.
He told Everton's official website: "I have a special relationship with the Chairman, Mr Kenwright, who did not want me to leave but this was an opportunity I could not refuse.
"I would like to place on record my thanks to everyone at Everton Football Club. The manager has been brilliant for me and helped make me the player that I am today.
"I would like to place on record my thanks to him and all the coaching staff and players who have worked with me since I joined the academy as a seven-year-old.
"Finally I would like to thank all the fans who have been amazing during my years at Everton. I have enjoyed every minute of my time there and I wish everyone at the club the best of luck for the new season and beyond."
Rodwell is poised to earn his third senior England cap in a midweek international friendly against Italy on Wednesday, August 15.