The move ends two years with City for the England midfielder who was signed from Everton by former manager Roberto Mancini.
Rodwell made 26 appearances in all competitions and scored twice for City.
Jack was a popular member of the squad and an enthusiastic contributor to the club's work in the community, delighting local children with appearances at several CITC events.
He made his debut on 19 August 2012 in the 3-2 win over Southampton which was one of 15 appearances in his first season at the Etihad Stadium.
Injuries limited the midfielder to just 10 appearances in the last campaign - a number which included three games in City's run to the Capital One Cup final.
The 23-year old joins fellow former Blues Adam Johnson and Costel Pantilimon under Gus Poyet at the Stadium of Light.
The Black Cats finished in 14th place in last season's Premier League table after their miracle escape from relegation which started at the Etihad Stadium where they claimed a surprise 2-2 draw.
They also finished at runners-up in the Capital One Cup after a 3-1 defeat to City in the final at Wembley.
Rodwell becomes their fifth signing of the summer, joining Pantilimon, Jordi Gomez, Billy Jones and Patrick van Aanholt in the North East.
Capped three times for his country, Rodwell has signed a five-year-deal with the Black Cats.
All at Manchester City FC would like to thank Jack for his contribution and wish him all the best for the future.