The court was told that 37-year-old Richard Smith was found dead at the home he shared with his wife Clair, 36, and sons Ben, nine and Aaron, 13 months.
Smith's body was discovered with his arms around the corpses of his wife and children. His dead wife was clutching the ashes of a baby boy they had lost four years earlier.
The inquest revealed that the couple were deeply affected by their son's death and each year took time off work to spend time together to remember him.
Richard Smith was said to have strangled and stabbed Clair before suffocating and knifing Ben and stabbing Aaron at their home in Pudsey, West Yorkshire.
It is reported he then placed the family on a bed, blocked doors and windows and set fire to the mattress before dying himself from smoke inhalation.
The coroner David Hinchliff said that mental health issues had made Smith carry out the killings.
He said: "He had undergone some aberration and problem affecting his mental health that caused him to take the action he did."
The coroner returned a verdict of unlawful killing on Clair and Ben and Aaron, and suicide for Smith.