The group first announced its intention to acquire Mey Içki in February, for an 'enterprise value' of $2.1 billion (£1.3 billion).
According to Diageo, the Turkish Competition Authority's clearance is conditional upon the subsequent disposal of the Mey Içki brands Hare liqueur and Maestro gin.
Diageo anticipates that these disposals will be completed within the current financial year.
In a statement Diageo said: "Mey Içki will be fully consolidated and transforms Diageo's existing position in this fast growing spirits market."
