Dutt replaces Matthias Sammer, who left to take up a similar position at Bayern Munich earlier this month.
The 47-year-old Dutt has agreed a four-year contract commencing on August 1 and will oversee the development of youth players and national team coaches.
"To take on this exciting task with the DFB has very special meaning," Dutt said in a statement.
"I look forward to working with national coach Joachim Low and all other DFB coaches.
"I feel it is incredibly exciting challenge."
Germany coach Low added: "I am glad that the DFB has found them competent solution.
"I'm looking forward to working together."
Dutt has experience coaching at the highest level in Germany having spent four years in charge of Freiburg until 2011. A later spell at Leverkusen ended with his dismissal in April this year.