The 19-year-old Germany Under-20 international spent just a single season with Dortmund, scoring once in five appearances following a move from Energie Cottbus.
Bittencourt has now been given a chance to establish himself as a regular by Hannover, who are happy to have the teenager on board.
"I am very pleased with the agreement. Leonardo wants to improve his skills in the Bundesliga and we gain a fast and strong attacking player," coach Mirko Slomka told the club's official website.
Bittencourt, who holds both a German and Brazilian passport, added: "I am a passionate footballer and my greatest wish is to show what I can do.
"I have a very good feeling Hannover is the right place for me."