The men, who were named locally as Robert Mcilwain, 73, and his brother John, 71, were found with stomach injuries possibly from a shotgun at the semi-detached house in the Gracemount area.
The men were found with serious injuries and were declared dead at the scene.
They had lived at the house in a quiet cul-de-sac, which is owned by the social care charity The Lockerby Trust, for about seven years.
Areas surrounding the property were cordoned off after police were called to a "disturbance" at around 5pm yesterday. Sources said police had received a call from a man who had said he was going to shoot himself.
Police are not looking for anyone else in connection with the deaths.
A neighbour said: "Someone called to say there had been an incident in the street. That's the first I knew of it, and then I saw police standing outside the door.
"Two brothers that lived there. They used to be gardeners but were retired. They'd been there a few years, they were just quiet, retired people and it's a quiet street."
Another resident added expressed frustration at the lack of information that was being made available to residents.
"There's been a lot of activity in the street, we wish someone would come and tell us what's going on," she said.
A Police Scotland statement said: "Police in Edinburgh attended a property in Lockerby Cottages near Gracemount at around 5pm this evening.
"On gaining entry, two elderly men were found seriously injured and were pronounced dead at the scene.
"Inquiries are continuing but police are not looking for anyone else in connection with this incident."
Most of the residents are thought to be elderly and the homes were originally built in the 19th century to house shareholders left ruined by the City of Glasgow Bank collapse of 1878.
A helicopter was involved in the response and there were road closures in the area south of the capital. Parts of Lasswade Road and other routes were shut, causing rush-hour delays.