Mr Gilham was placed on a five-year good behaviour bond after pleading guilty to his brother's manslaughter in 1995.
The civil engineer said he had been provoked into stabbing him after Christopher confessed to killing their parents and then setting Helen's body alight.
Mr Gilham's barrister, Clive Steirn, SC, put forward numerous grounds of appeal, including the finding, after the trial, of an apparent blood-stained fingermark on an intercom which the court heard corroborated Gilham's account of what happened.
Other grounds related to the crown's claimed timing of the deaths and the fire.
An expert, who carried out the 1993 autopsies, told the appeal he now had a different view relating to findings of carbon monoxide in the bloodstreams of the parents and Christopher.
Dr Christopher Lawrence said he now accepted they all may have been alive when the fire started, which contradicted the crown case.
Mr Gilham clasped hands with his wife Rebecca as Justices Peter McClellan, Elizabeth Fullerton and Peter Garling handed down their judgment, which was two to one in favour of an acquittal.
The couple then exchanged a lengthy embrace and Ms Gilham wiped tears from her eyes.
In a brief statement outside court, Mr Gilham thanked his supporters and "everyone who fought for the truth to be told''.
"This has been a horrendous experience for us. I'm glad today that I've been acquitted of the charges,'' he said.
"I'd like to thank all our supporters who have stuck by me and most importantly my wife Rebecca and my children.
"I am very happy to be going home a free man.''
Ms Gilham added, "I'm just thrilled to be able to tell our girls that daddy is never going back to prison''.
-AAP
