The 23-year-old joins the German champions for an undisclosed fee after signing a four-year contract.
Schieber caught the eye in March when he scored two goals for Stuttgart in a thrilling 4-4 draw at Dortmund. Aside from those two goals, Schieber has only one other league goal to his name in 22 league appearances for Stuttgart.
However, he spent the 2010-11 campaign on loan at Nuremburg where he scored seven times in 29 appearances.
"We are delighted to have signed a young German player in Julian Schieber," said Dortmund's director of sport Michael Zorc. "He fits perfectly into our team and has huge potential."
Schieber is the second major attacking addition to the Dortmund squad, following the signing of Marco Reus from Borussia Moenchengladbach.
Midfielders Mustafa Amini, Oliver Kirch and Leonardo Bittencourt have also been signed as Dortmund prepare to win a third consecutive title next season.