22-year-old Valentina Marie Strabach pleaded not guilty after Murray Vernon
Quartermaine was stabbed more than 200 times with a pair of scissors at his home in Western Australia state in January 2011.
"I conclude that... the accused was insane at the time of the killing of Mr Quartermaine and is not criminally responsible for her actions," Supreme Court of Western Australia Commissioner Kevin Sleight said in his judgement.
Under questioning by police, Strabach, who had arrived in Australia only weeks before the killing, said she felt compelled to kill Quartermaine because she held the delusional belief that he was a paedophile.
She said she the met 79-year-old when she was lost, and he offered to give her a lift to where she was staying. She then asked to go to his home because she wanted to see if he was a child sex offender.
Once there, Strabach found a pair of scissors which she used to stab him repeatedly, leaving him with chest wounds, and perforating his lungs, bowel, liver and jugular. She also amputated his genitalia and both his big toes.
Sleight said he was satisfied Strabach was suffering from a mental illness in the form of paranoid schizophrenia at the time of the murder, and she was influenced by hallucinations ordering her to kill.
"It must be stressed that there was absolutely no basis for the accused concluding that Mr Quartermaine was a paedophile," Sleight said."However, in her psychotic state the accused had developed a delusional obsession about paedophilia."
The court was told that Strabach, reportedly a dual Australian-French citizen, had previously sought medical help in France and was prescribed strong medication, but stopped taking it as she was unable to function properly.
She will be detained at a mental health hospital in Perth until she is released by an order of the Western Australian governor.