The 22-year-old only joined Burnely from Chelsea last summer, but following their relegation, he has now left.
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The midfielder made 38 appearances across all competitions for Burnley, scoring three goals and providing one assist in the process.
Ugochukwu becomes the latest addition for Turkish giants Galatasaray, joining on an initial loan €3 million loan fee with a conditional buy option of €22.5 million should he make 25 appearances.