In a statement, Dortmund confirmed: "Attacking player Emre Mor leaves Borussia Dortmund after a year and moves to Celta Vigo at his own request.
"The player, who grew up in Denmark, asked Borussia Dortmund for the move because he hopes to be at another club with greater opportunities than there are in BVB's already well-stocked attack."
Sporting director Michael Zorc added: "We respect this wish and we wish Emre all the best for the future."
Mor, who joined Dortmund from Nordsjaelland last year, could make his debut for Celta against Alaves on September 10.
The news follows Celta's confirmation that Claudio Beauvue has sealed a move to Leganes for the rest of the season.