Police said there was no suspicious circumstances surrounding the death of the man, who was from the Scottish Borders.
His family have been informed.
The grisly discovery, unearthed at Pollock Halls on September 26, had been there for a “considerable length of time”.
Police Scotland said: “Following scientific examination, the remains found at Pollock Halls in Edinburgh on 26th September have now been identified. There are no suspicious circumstances surrounding the death of the man, who was in his 50s and from the Scottish Borders. His family have been informed.”
Forensic teams probed an area in front of Fraser Court accommodation block at the halls on Dalkeith Road after police were notified of the find.
A cordon was in put in place as officers and a forensic teams remained on the scene.
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