John and Elizabeth Knott from Bosbury, in Herefordshire, were found dead at their home in August. Each had died from a single shotgun wound.
A shotgun registered to Mr Knott, 71, was recovered by police at the scene.
Assistant Coroner Roland Wooderson recorded a verdict of unlawful killing for Mrs Knott, while finding Mr Knott intentionally took his own life.
The couple's daughter Elizabeth Conway said she was shocked, but not surprised.
"Mum didn't want to continue to live like that and Dad couldn't see a life without Mum," she said in a statement.
The inquest, sitting at Hereford Town Hall, heard Mrs Knott, 70, had been suffering from Alzheimer's disease and anxiety.
Friends described how Mr Knott had been devoted to his wife, known as Anne, and had been upset when she attended a nearby respite care home.
A couple of days after arriving at the care home, the inquest was told Mr Knott arranged for his wife to return home and two days later the couple were found dead.
Relatives alerted police after becoming concerned about them.
They were found in a workshop at the back of their garage. The door had been locked from the inside and the handle removed.
Giving evidence, Det Sgt Tim Powell said there was no sign of any third-party involvement.
The inquest also heard Mr Knott had been concerned by plans by travellers to move on to land next to their home.
A man shot his ill wife before killing himself in a suicide pact, an inquest has heard.