As part of the deal, Dortmund retain an option the buy back the attacking midfielder when his contract at Hanover expires.
The 19-year-old German, who joined Dortmund from Energie Cottbus in 2012, made five league appearances last season, scoring once, and also played one game in the run to the Champions League final.
Bittencourt, who is of Brazilian descent, has also played for Germany at several junior levels including the Under-21 team.
Hanover finished ninth in the Bundesliga, missing out on a Europa League spot after three seasons of continental football.
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