Kenneth Graham, 52, was found covered in blood in the kitchen of their semi-detached house in South Queensferry, West Lothian, while his wife Donna, 51, was upstairs in bed with a pillow next to her.
Laura Graham, 27, who needed the help of a neighbour to get into the home, emerged from the semi-detached house on Sunday and was so shocked she ran into the street screaming, neighbours said.
The couple were due to celebrate their Pearl wedding anniversary next Monday.
Police confirmed that officers were not looking for anyone in connection with the deaths.
Detective Chief Inspector Gary Cunningham added: "This is a tragic event and our thoughts are with the immediate family and friends of the victims.
"We still have some investigations to carry out, and police are likely to be in the area for the next few days. However, I can confirm we are not looking for anyone in connection with these deaths."
One neighbour told what happened when Laura Graham arrived at the house in Echline Gardens on Sunday afternoon.
"The eldest daughter arrived and couldn't get in," he said. "The front and back doors and conservatory were locked.
"So she went to a neighbour's to get the key. When they walked in they found the man in the kitchen covered in blood. There was also blood all over the walls.
"When they went upstairs they found the woman in the bed with a pillow next to her.
"She was dead. It seemed like he had killed her, but we are really not sure."
The bodies were found about 5pm. A dog was also thought to be in the house at the time.
Another neighbour added: "After the police arrived the daughter was in the street screaming. She wanted to get the dog out of the house.
"The police were there all night and you could see the flashes coming from them photographing the scene.
"We really feel for the daughters. We don't know the family personally, but they have been here a really long time and seemed like a really normal family."
The couple married at St Stephen's Comely Bank Parish Church, Edinburgh, in March 1984, and lived close to the city centre until they moved to South Queensferry.
Mr Graham is thought to have worked as a sales executive and printer. The couple also have a daughter Lisa, 23.
Another neighbour said: "They have lived in the area for a really long time and almost everyone knew them. They used to go out for walks quite a lot during the summer and would always say hello to everyone.
"We have heard there is not anyone else involved in causing their deaths. It is more a tragic event than anything else. Our thoughts are with their two daughters."
Another resident told how they came home from work "just as the first two police cars came speeding down the road with their lights on".
She added: "There were lots of officers around overnight.
"We are quite new to the area and did not really know Donna and Kenny, but they always seemed happy enough and would say hello."
Police Scotland's Major Investigation Squad is probing the deaths and officers were still at the scene yesterday. The house and a lane running behind it were cordoned off.
The cul-de-sac, which is in an upmarket area of the town, was quiet yesterday as residents said they wanted to "stay out of the way."
Officers continued to conduct door to door inquiries while forensics teams worked at the property.
One body was removed by private ambulance. As it drove away, some neighbours stood outside crying.