Justice Powell remanded Yates in custody at the Mason Clinic ahead of another hearing.
Yates, 32, who was wearing a black hoody, sat silently in the dock looking towards the floor throughout.
In March last year he was found fit to stand trial, though he spent his time on remand in a secure psychiatric facility.
Crown prosecutor Henry Steele said the weight of the evidence in the psychological reports was such that the only reasonable verdict was a finding that the facts were proven, but Yates was not criminally responsible.
Justice Powell agreed.
“There is no dispute on the evidence before me that Mr Yates killed his uncle,” the Judge said.
He admitted the killing to police and medical staff and was found fit to enter his plea of not guilty by reason of insanity.
Justice Powell said he was satisfied Yates was insane at the time of the killing.
“He did not know that his actions were morally wrong.”
He was formally acquitted of the murder charge. His fate will be decided at a later hearing.
Members of the Yates family were in court for the finding. Justice Powell expressed his sympathy and apologised for having to read the gruesome facts of the case for them to hear.