The Bundesliga giants have opted to cash in on the promising youngster, but have the option to re-sign him for a set fee
The 19-year-old has signed a contract until June 2017 with his new club and will be wearing the No.32 jersey at Hannover, but BVB have inserted a buy-back clause in the deal, meaning they can re-sign the player for a set fee.
"I am a very passionate player and I want to show as often as possible what I can do. I have a great feeling about Hannover and feel that this is the right club for me at this stage of my career," the Germany Under-20 international said.
"My friend Andre Hoffmann is proof that young players can make a name for themselves at Hannover and that is my goal as well."
Bittencourt is a product of the Energie Cottbus youth academy and joined Dortmund in the summer of 2012.
He failed to make an impact with the Champions League finalists, though, as he made only five Bundesliga appearances for BVB, scoring once in the process.