The 18-year-old moves from Danish first division side FC Nordsjaelland and has signed a five-year contract.
Mor was born in Denmark and represented the international side up to Under-19 level where he switched to Turkey. The midfielder made his senior debut last month and has earned a place in Turkey’s squad for Euro 2016.
"Emre Mor is a highly gifted and on the offensive versatile young players with huge potential for development," said Dortmund’s sporting director Michael Zorc.
Ahead of the new season, Dortmund have already completed the signings of Sebastian Rode, Ousmane Dembele, Marc Bartra and Mikel Merino.