The 60-year-old woman was found dead in her living room at the ground-floor flat in Comiston Gardens just after 1900 GMT on Monday.
A spokesman for Lothian and Borders Police said the woman was the only person in the flat at the time.
A neighbour called 999 after hearing the woman's fire alarm. The blaze is not thought to have been suspicious.
Tom McGrath, Lothian and Borders Fire and Rescue service group manager, said: "There was a lot of smoke damage particularly in the living room.
"We checked the flats above and to either side but they weren't affected and nobody had to be evacuated.
"A neighbour who heard her fire alarm went up to one of her windows and felt they were overly warm so called the fire brigade."
Source: BBC News
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