The Bundesliga title holder announced the capture of the talented midfielder, who has represented his homeland at Under-19 level.
The 17-year-old has been closely linked with BVB in the last month, and the Ruhr side announced via its official Twitter account that the Germany Under-19 international, who also has Brazilian nationality, had agreed to a four-year contract.
"We have watched him since his first game in the 2. Bundesliga. He is an outstanding talent, and we feel that he will fit perfectly into our philosophy," BVB sporting director Michael Zorc told Sky Sport News HD.
Neither Cottbus nor Dortmund have disclosed any financial details regarding the transaction, but reports suggest a release fee in the region of 3 million euros.
Bittencourt has made 12 appearances for Cottbus in the 2. Bundesliga this season, scoring two goals.