He made 22 appearances for England, scoring six goals.
Hamann joined City three years ago in bizarre circumstances having signed a pre-contract agreement with Bolton before changing his mind and telling the club he wanted to head to Eastlands instead.
The German scored one goal in his 53 starts while at City, the solitary strike coming in the first game of 2008/09 against EB/Streymur.
A toe injury ruled him out of most of the last few months of the season.
Ball was offered a City contract by former boss Stuart Pearce after impressing in a short trial after his departure from PSV Eindhoven.
He quickly established himself as first-choice left back until the arrival of Javier Garrido the following summer saw him have to battle for his place under Sven-Goran Eriksson's management.
Mills joined City from Leeds in July 2004 and had loan spells at Hull City, Charlton and Derby.
While at Pride Park he picked up a serious knee injury in January 2008 and he has not played since.
Matthew Brown, Ian Daly, Gregor Hartley, Ben Morris, Curtis Obeng, Chris Ramsey and Angelos Tsiaklis have also left the club.
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