The bodies of 52-year-old Geraldine Newman and her two children, 11-year-old Shannon and six-year-old Shane, were found at their Beeston Way home on February 2, 2016.
The body of their father, Paul Newman, 42, was found dead at the foot of cliffs in Anglesey, Wales, hours later.
The inquest at Wakefield Coroner's Court this morning heard that a police investigation had found that Mr Newman had killed his family before travelling to Wales and leaping from a cliff with a 240-foot-drop.
Details of their death found that Geraldine Newman had died from severe head injuries caused by a hammer.
Her body was found on the couch of the living room. The children were found in their beds and had suffered multiple stab wounds.
A letter was found in the kitchen in Paul's handwriting, and although he did not admit to the killings the word 'sorry' was included in the note.
Blood-stained clothing belonging to Paul was found in the bathroom while blood found on a light switch matched that of Shane's and matched Paul's fingerprints.
Senior coroner Kevin McLoughlin said that an emergency service worker who worked at the scene suffered post traumatic stress disorder (PTSD) over what they saw and had been forced to take months off work.
It was thought that Mr Newman had killed his family sometime on February 1.
He had even phoned the children's school to inform them that they were feeling unwell and would not be attending that day.
He was seen leaving the Beeston Way home between 11.30am and 12 noon on February 1, 2016, and travelled to Castleford in his Toyota Yaris.
He withdrew £250 from an ATM and travelled to Leeds Railway Station, where CCTV picked up his movements.
He then bought a ticket to Holyhead in Wales and boarded a train.
Shortly before 2pm he accidentally took a photo of himself on Geraldine's phone which had a security app installed that takes a snap if it suspects that a person is trying to access the phone who is not the owner.
The photo was then automatically sent to a friend of Geraldine's who became suspicious.
Paul arrived in Anglesey shortly before 4pm and the inquest heard that he read a text message sent to him shortly after 7pm.
At 9pm his red jacket was found near the cliff edge containing £180 and was handed into a police station the next morning.
Paul's body was found on rocks 240 feet below at 5.25pm the following day. He was only wearing his underpants and socks.
Recording a death of suicide, coroner Kevin McLoughlin said: "A fall of that magnitude would make death a virtual certainty.
"I reject the possibility that he slipped or a third person was involved. The conclusion of suicide is appropriate."
Addressing the death of Geraldine and the two children, he said: "I'm in no doubt that all three were unlawfully killed at home on or about February 1, 2016.
"They were killed by another person without justification."