The Tunisian defender arrives to plug the gap left by the departure of Serdar Tasci to Spartak Moscow on Friday and becomes the third player to swap Hannover for Stuttgart this summer, following Mohammed Abdellaoue and Konstantin Rausch's arrivals from Baden-Wurttemberg.
"The transfer of Karim Haggui is part of our consequential efforts to reduce the size of our squad," said Hannover's director of sport Dirk Dufner. "That is why we were able to grant his wish of making a quick change."
Hannover coach Mirko Slomka praised Haggui's reliability and the status he enjoyed within his squad.
"He was a key player for us as well as an extremely nice chap," he said. "That is proven also by the fact that his team-mates regularly elected him on their team representative panel."
Haggui has signed a two-year contract in Stuttgart, joining for an undisclosed fee.
"Karim brings a great deal of experience with him, both in the Bundesliga and in Europe, and we hope that he settles in quickly and strengthens our squad accordingly," said Stuttgart's director of sport Fredi Bobic.