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.
He is the youngest ever player to play for Turkey at a European Football Championship. The 18-year-old footballer is the third youngest player at EURO 2016 behind England's Marcus Rashford and Portugal's Renatos Sanches, though only by a matter of months.
"(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."
Emre Mor has lived all his life in Denmark and only received Turkish citizenship this year after receiving authorization from his jailed father. Yet the fleet-footed winger, unknown to most Turkish football fans at the start of 2016, has in just weeks become one of the great hopes for Turkey at the European Championship finals. Mor's reputation grew again when Borussia Dortmund signed him from Danish side Nordsjaelland. Mor, who had played for FC Nordsjaelland since 2015, appeared for Denmark's youth side but switched his allegiance this year following an intervention by Terim.