The 57-year-old's body was found after firefighters put out the blaze at Standford Hall flats in Allison Drive.
The emergency services had been called to the incident at about 17:30 on Friday.
Police have said inquiries are under way into the cause of the fire but there do not appear to be any suspicious circumstances.
A man has died in a house fire in Cambuslang, South Lanarkshire.