Police made the discovery after they were called to a house in Parkgrove Terrace in Clermiston at about 21:30 on Sunday.
Officers have confirmed they are investigating an "unexplained death".
A Police Scotland spokeswoman said: "Inquiries are ongoing and the death is currently being treated as unexplained. A report will be sent to the procurator fiscal."
The body of a 56-year-old woman has been found in a house in Edinburgh.