The 20-year-old has also penned a new deal at Dortmund, tying him down until June 2017.
"He needs to play over the course of the next two seasons," explained BVB sporting director Michael Zorc, before expressing his joy at extending the youngster's Dortmund stay.
Leitner, who has made 42 Bundesliga appearances for Dortmund, was no less satisfied. "Stuttgart are a superb club with great tradition. I think we can achieve a lot here. I really want to see where they can go and am looking forward to playing my part."