Galatasaray said in a statement on Borsa Istanbul that the clubs agreed on the temporary transfer of 31-year-old Durmaz for the 2020-21 football season.
Fatih Karagumruk will pay Galatasaray 2.6 million Turkish liras ($334,390) transfer fee.
Durmaz was the 2010 Swedish champion with Malmo.
He won back-to-back Greek league title with Olympiacos in 2015 and 2016. The Swedish international had 17 appearances for Galatasaray.
In addition to Malmo, Olympiacos and Galatasaray, Durmaz played for Turkey's Genclerbirligi and French club Toulouse.
