The Turkish winger is set to fulfill his dream of competing abroad after several months of negotiations between his club and the Spanish capital side
The deal will see Galatasaray receive €12 million, plus €1m in the form of bonuses, for Turan, who will sign a four-year contract with the Spanish club.
The Turkey international has long been a target of Atletico, with Galatasaray first announcing in March they had begun negotiations with the Spanish capital club for the transfer of the 24-year-old.
Talks between the two clubs then hit a brick wall, but Atletico never stopped keeping an eye on Turan, who is keen on proving himself in a more high-profile league.
A product of Galatasaray's youth ranks, Turan will complete the move after Turkey's friendly against Estonia on Wednesday.