The 18-year-old forward has been linked with major clubs from across Europe, including Premier League champions Leicester and Europa League finalists Liverpool, but Dortmund have won the race for his signature.
Dembele has represented France at every youth level and has scored 12 goals in 25 appearances in his debut season with Rennes, securing the young player of the season award in Ligue 1.
Dortmund sporting director Michael Zorc said: "Ousmane can play nearly every position in attack. He is strong one-on-one, he can play with both feet and he is fast and dangerous in front of goal."
Chief executive Hans-Joachim Watzke told the club's website: "He has always given us the impression that he does not wish for anything else other than to play our intensive football for our special club in our unique stadium."