Fire crews were called to Glen Moy, in the St Leonards area of East Kilbride, shortly after 6.30am.
Neighbours raised the alarm on hearing screams after the blaze broke out in a ground floor flat.
In the second fire in the street in less than two weeks, emergency services rushed to the flats and three people were taken to nearby Hairmyres Hospital while five more were treated at the scene.
Station Commander Jim Anderson, of Strathclyde Fire & Rescue, said: "Four firefighters donned breathing apparatus and entered the burning flat.
"The crews, who were working in thick smoke and extreme heat, very quickly located the occupier, who was sadly confirmed as a fatality."
A joint investigation into the cause of the fire will be held by Strathclyde Fire & Rescue and police.
A woman living in a neighbouring block of flats said she had heard screaming early today but thought it was a couple arguing.
The woman, who asked not to be named, said: "Eventually, I looked out of the window as the screaming had become louder and in the street I saw a woman dressed in pyjamas, calling for help.
"The fire brigade was there within minutes but we knew there was someone in the ground floor flats as we kept seeing torchlights through the window; it looked like they were searching for a person.
"It was awful to see.
"They say everything comes in threes but I hope this is our last fire here. It is a nice area."
This morning a green tarpaulin covered the window of the ground floor property in which the person is thought to have died.
Police have sealed off the entire block as forensics officers begin investigating at the scene.
A police spokeswoman said: "Our officers were called to attend an incident at a block of flats in Glen Moy at around 6.30am today- officers are still at the scene."
The fire is the second to hit the St Leonards community this month.
A total of 10 people had to be rescued from a neighbouring Glen Moy block of flats on Sunday, November 4. Police are treating this blaze as deliberate.
The fire was started on the second floor of the building, causing residents living in the floor above to become trapped.