Mother-of-two Sheena Jackson, 58, was found dead in the couple’s cottage in Cambusbarron, near Stirling, by colleagues concerned she had not turned up for work.
Her husband Alex, 65, known as Ash, was found “seriously ill” upstairs and taken to hospital where he later died.
Detective Chief Inspector Jim Thomson, from Forth Valley CID, said: “Following the deaths of a 58-year-old woman at an address in the Main Street area of Cambusbarron on Tuesday 30 October and the subsequent death of a 65-year-old man who was found seriously unwell within the property, a thorough police investigation was launched that has now concluded.
“The woman was formally identified as Sheena Jackson and following a post mortem examination, her death was established as murder.
“The man was formally identified as Alexander Jackson and his death was not suspicious. We are satisfied this incident was contained to within the property and we are not looking for anyone else in connection with the deaths.”
The cottage and its adjoining close were cordoned off with police tape in the aftermath of the incident. A lone double-rose floral tribute was placed at the couple’s white-painted front door.
Near-neighbour Tony Ross, 68, said co-workers at the Department for Work and Pensions in Alloa, where Ms Jackson worked, had raised the alarm after she failed to turn up for work.
He said: “A colleague from Sheena’s work had come to check on her when they couldn’t get her on the phone.
“They thought they’d better go round. They got no answer at the door, so they went to the back door, tried it, and it was unlocked, and she went in and found them.” Mr Ross, who has lived in Cambusbarron for 20 years, said the Jacksons were well known in the small Stirlingshire village.
He said: “They were very pleasant people. With it being a village, you’re always bumping into one another and everybody knew them to say hello to. We’re all really shocked.”
Friends said Ms Jackson kept fit by walking her dog and had even completed the West Highland Way in recent years, but her husband suffered from heart trouble and had a pacemaker fitted.