Haggiu has started three of Hannover's four Bundesliga games this season, but the club have allowed him to become the third player to leave for Stuttgart this summer following Mohammed Abdellaoue and Konstantin Rausch.
Hannover director of sport Dirk Dufner has insisted that Haggui wanted to leave for Stuttgart once an offer was on the table, with the club forced to trim their squad by financial constraints.
Dufner told reporters: "The transfer of Karim Haggui is part of our consequential efforts to reduce the size of our squad. That is why we were able to grant his wish of making a quick change."
The 29-year-old arrives in Stuttgart with considerable experience of German football after making more than 150 Bundesliga appearances during seven seasons with Hannover and Bayer Leverkusen.