The 51-year-old Dutt is the third top official of VfB Stuttgart to lose their job after the club's demotion to the second division was sealed with a 1-3 defeat by VfL Wolfsburg last Saturday.
The club's chief coach Juergen Kramny was removed from his post with immediate effect on Sunday and its president Bernd Wahler laid down his office on the same day.
Dutt and the supervisory board of VfB Stuttgart have agreed after intensive discussions that that he will "leave the club to enable it a new beginning", supervisory board chairman Martin Schaefer said in a statement yesterday.
"It will be certainly wrong to put the blame entirely on him for the negative developments," the statement said.
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The supervisory board also announced the appointment of Bundesliga second division coach Jos Luhukay as the new chief coach of the club. Luhukay is credited with taking several second division clubs to the top flight of German football.
His experience in this area was a main consideration for his appointment, VfB officials said.
Luhukay's immediate task is to train the VfB team for its first Bundesliga second division campaign since 1975, which begins within four weeks.
The northern German club's leadership blamed him for its poor start in a new national championship season and for its plunge to the bottom of the Bundesliga table by losing all nine matches played.
Born on January 25, 1965 in Cologne as the son of an Indian migrant and a German mother, Dutt developed a passion for football at a very young age and after playing in the junior teams of some football clubs near Stuttgart, where he grew up, he worked his way up to the top levels of the national league.