The young striker pens a contract until 2016 with the German champions, who becomes their fourth arrival of an increasingly busy summer at Signal Iduna Park
The 23-year-old, who graduated from the Roten's youth ranks, has agreed a four-year deal with Jurgen Klopp's side and seemingly replaces Lucas Barrios as cover in attack.
Speaking about the move, Dortmund sporting director Michael Zorc said: "We are delighted to add a young German player that fits perfectly in our team. He has a great future."
However, Schieber is yet to undergo a medical, although it is expected to be a formality for the ex-Germany Under-21 striker, who scored three times in 18 Bundesliga appearances for Stuttgart last season.
Details about the forward's transfer remain unknown, but it is claimed that a fee in the region of €6-8 million has been paid out by BVB.
He becomes Dortmund's fourth capture of the summer, following Marco Reus, Leonardo Bittencourt and Oliver Kirch.