Leitner is clearly highly regarded at the Westfalenstadion as the Champions League runners-up have signed the 20-year-old to a four-year deal.
But he will spend the first two years in south-west Germany with Stuttgart, who finished 12th in the Bundesliga last season.
"We are delighted that Moritz Leitner will now wear the jersey of the VfB," said sporting director Fredi Bobic on Stuttgart's official website.
"He fits in perfectly with our requirements. He is young, technically gifted and has a very good understanding of the game.
"And not least, he can be used in several positions, thus he has all the skills to play a key role in our game."
Leitner joined Dortmund, who confirmed on their official website that the youngster had agreed a new contract, from 1860 Munich in 2011 and made 30 appearances in all competitions last season, most of which came from the bench.
The Westphalian club feel Leitner could benefit from nailing down a first-team spot with Stuttgart.
"I think we can achieve a lot here, I have a great desire to see the VfB where it belongs and I would like to do my part," he said.