The 39-year-old, who played 42 times for his country between 1995 and 2003, became the first Turk to coach a Bundesliga side on a permanent basis after replacing Mirko Slomka, who was sacked last week.
It is also the first senior coaching job for the former midfielder who previously worked as a youth team coach at Real Socieded, Hoffenheim and VfB Stuttgart and as assistant to Turkey coach Abdullah Avci between 2012 and 2013.
"This appointment has been taken with the future of Hanover 96 in mind," sporting director Dirk Dufner told the club website (www.hanover96.de).
"We have decided for a young, well trained and highly motivated coach and he has fully convinced us with his personality.
"We know that we are making a bold decision, but look on our co-operation with Tayfun Korkut with a great perspective. I have great confidence that we will be successful together."
Hanover, 13th in the 18-team table, parted company with Slomka after almost exactly three years with the team only four points clear of the relegation zone.
"I thank Hanover for their trust in giving me this chance," said Korkut, who was born and raised in Stuttgart and began his playing career with Stuttgarter Kickers.
He went on to play for Fenerbahce, Real Sociedad, Espanyol, Besiktas and Genclerbirligi.
Hanover are the fourth Bundesliga club to change coach this season after VfB Stuttgart, Hamburg SV and Nuremberg. Their next competitive game is at VfL Wolfsburg in the league on January 25