Dutt was sacked as coach of Bremen in October but negotiations continued with regards to his contract, which was due to expire in June 2016.
However, Bremen have confirmed the mutual termination of the deal and Dutt has been heavily linked with taking over from Fredi Bobic at Stuttgart as sporting director.
Bobic left the club in September, with Bremen stating their eagerness not to stand in the way of Cologne-born Dutt taking on the role at the Mercedes-Benz Arena.
"The talks about the contract termination went very fairly just like the entire collaboration," said Bremen's manager of sport Thomas Eichin.
"We always made it very clear that we really value the work of Robin Dutt and his team and don't want to stand in the way should something come up for a new challenge for Robin.
"Robin Dutt did important work for us. We wish him all the best for his new endeavours."
Dutt left his position in charge of Bremen after the side failed to win any of their opening nine Bundesliga games.
Huub Stevens' Stuttgart are 15th in the German top flight, one place above Bremen.
