Hamann, capped 59 times by Germany during his playing career, undertook his first management assignment at Edgeley Park this summer following County's relegation from the Football League.
His appointment to replace Ray Mathias coincided with the promise of new investment in the club from Liverpool-based businessman Tony Evans.
All over: Dietmar Hamann has quit as manager of Stockport County
However, a deal failed to materialise and after three league wins in 19 attempts, Hamman cited the collapse of Evans' takeover bid as a key factor in ending his four months in charge.
In a statement on Stockport's official website, Hamman said: 'Following a meeting this morning between (chairman) Lord Snape and myself, I have tendered my resignation as manager of Stockport County.
'Having been introduced to the club by Tony Evans, I presumed that the takeover by him and his consortium would have taken place.
'Various promises were made to me at the time of my appointment which subsequently did not take place. I feel therefore unable to continue in the post.'
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