The 36-year-old was discovered inside the East Kilbride property.
Fire and rescue teams were called out to the tower block at Phoenix Court at at around 9pm on Saturday November 23 after reports of a fire.
Firefighters ensured the blaze was extinguished and searched neighbouring flats to check that the fire had not spread.
A joint investigation into the circumstances surrounding the blaze has been launched by the Scottish Fire and Rescue Service (SFRS) and Police Scotland.
The fire is not being treated as suspicious.
An SFRS spokesman issued a warning to people.
He said: "Any death through fire is a tragedy and we must all recognise the need to prevent it happening in our homes.
"Fire can strike anywhere. Every home must have working smoke alarms, doors should be closed fully at night, and cooking appliances and smoking materials must never be left unattended while they are in use.
"If you or someone you know could benefit, then please contact us by calling our freephone number: 0800 0731 999 or texting 'check' to 61611."
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