The midfielder was deemed surplus to requirements at the Etihad Stadium and has signed a five-year contract with Gus Poyet's side as he looks to revive his career
The 23-year-old midfielder has signed a five-year contract with Gus Poyet's side, with the Black Cats having agreed a fee in excess of €12 million with the Premier League champions.
Rodwell has been capped three times by England but was deemed surplus to requirements at the Etihad Stadium following the club's decision to sign Frank Lampard on loan.
The former Everton midfielder joined City in 2012 but started just seven Premier League games in two seasons at the club, having been beset by injuries.
Poyet remains keen to strengthen his squad and is believed to be closing in on a deal to re-sign Santiago Vergini on loan, while he retains an interest in Liverpool striker Fabio Borini.