The 71-year-old was found dead in her 11th floor flat at Sherry Heights in Cambuslang, South Lanarkshire. She was named locally as Maureen Kane.
Fire crews were alerted around 1.35am today and teams from Clydesmill and Polmadie were quickly on the scene.
Six firefighters, wearing breathing apparatus, entered the property and quickly extinguished the blaze.
Following a search of the property, crews discovered the body of the elderly woman.
Today investigations are continuing at the 12-storey block, but it's thought the blaze was not suspicious.
A fire crew was standing by and a fire investigation unit arrived at the scene around mid morning.
There was visible smoke damage around the windows where the fire had broken out towards the side and rear of the building.
However, the blaze did not appear to affect neighbouring properties.
One woman, who did not want to be named, had known Mrs Kane for around 20 years.
She said: "It is very sad to hear what happened.
"We were friends for a number of years and enjoyed a few holidays together.
"She lived alone and lately had been suffering from arthritis.
"She was retired from her job as a school teacher and played the chapel organ for a number of years."
Another woman had called round to see if her boyfriend's grandfather, who lives in the block, was all right.
The woman said: "We heard about the fire this morning. My boyfriend's grandad lives on the eighth floor, but didn't seem to have been affected by it.
"It's very sad that something like this has happened."
Assistant Chief Officer David Goodhew, of Strathclyde Fire and Rescue, said: "Our thoughts are with the family and friends of this lady at this time.
"Our investigation section are currently working with colleagues from Strathclyde Police to determine the cause of the fire."