The La Liga club did not disclose the fee for the player, although media reports said that the 20-year-old was purchased for a club record 13 million euros ($15.6 million).
Mor, who has played 12 times for the Turkish national team, only joined the Bundesliga side in June of last year but impressed in 19 appearances in all competitions last season.
"(Mor) is one of the young players with the most potential in European football," said Celta in a statement. "(He) stands out for his enormous one-on-one ability and his great speed, which gives him an impressive capacity to overload opponents, as well as the ease with which he passes between the lines."
Dortmund also sold French youngster Ousmane Dembele to Barcelona last week, but signed Ukraine winger Andriy Yarmolenko from Dynamo Kiev on Monday to bolster their squad.
(Reporting by Rik Sharma; Editing by Christian Radnedge)
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