Korkut, 39, moves from being assistant Turkey coach to take over from Mirko Slomka, who was sacked on Friday after a string of disappointing results.
Hannover said Korkut, a former midfielder capped 42 times by Turkey, was "the first coach of Turkish origin in the history of the Bundesliga", and signed a contract until June 30, 2016.
The club currently sit 13th in the German league.
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