Robert McIlwain, 73, and his brother John, 71, were found with serious stomach injuries, possibly from a shotgun, at their semi-detached home in the Gracemount area of Edinburgh, last week.
The men were declared dead at the scene but Police Scotland only formally named them yesterday, five days after the tragedy.
The force confirmed there were no suspicious circumstances surrounding the men's deaths, and detectives are not looking for anyone else in connection with the incident.
But police have called on anyone who might have information about their next of kin to contact them.
The brothers 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" on Thursday evening.
Sources said police had received a phone call from a man who had said that he was going to shoot himself.
A helicopter was involved in the response and there were road closures in the area in the south of the capital.
Parts of Lasswade Road and other routes were closed, which caused rush-hour delays.
Residents reported they had seen armed officers entering the building, while a police helicopter circled overhead, and two ambulances were also called to the scene.
Neighbours said the older brother was heartbroken after illness left him unable to tend his beloved garden.
It is understood the older Mr McIlwain had cared for his disabled brother for a long time but his own health had began failing in the last 18 months as he battled pulmonary fibrosis linked to asbestos exposure.
The pensioner had to hire a professional to carry out the work instead.
The brothers had also been keen golfers, but were no longer able to play because of their declining health and mobility.
One neighbour had revealed how her husband had been expecting to witness the men's wills. She added: "The way that everyone spoke it sounded like they were realising the end was near."