Jethro Curtis, 44, attacked Stephen Curtis, 63, in their Maffra home, about 220km east of Melbourne, on the evening of January 18.
He had accused the older man of physically and sexually abusing him and other members of their family, although the allegations have not been proven.
The day before the murder, Curtis contacted Stephen's wife about the accusations and said the older man's days were numbered and it would all be over soon.
Then on January 18, while his mother was out of the house, Curtis smoked cannabis, methamphetamine and took prescription anti-psychotic medication before walking into Stephen's room about 9pm.
He repeatedly punched Stephen in the face and kicked him in the head, before rolling him onto his stomach and fatally strangling him with a telephone cable.
After the murder, Curtis logged into Stephen's bank account and transferred himself $5000.
He also stole Stephen's car, drove it to a nearby shopping centre and left it in an underground car park before boarding a train to Pakenham.
Curtis withdrew another $4000 over the next few hours and admitted to killing Stephen in conversations with his former partners and then his mother.
His mother called triple zero after she was notified.
Paramedics arrived at the Maffra property about noon on January 19 and found Stephen's body on the ground and covered in a shower curtain.
When arrested 205km away in the Melbourne beachside suburb of Seaford, Curtis immediately admitted to killing his uncle, telling detectives he snapped and believed Stephen was a child molester.
He pleaded guilty to murder in July.
Curtis did not react on Wednesday as Victorian Supreme Court Justice Rita Incerti handed down his sentence.
She described the murder as a brutal attack, noting Stephen had been particularly frail because of his Parkinson's disease.
"The offending was extreme," the judge said in her sentencing reasons.
"It was carried out against a frail and defenceless victim in his own home."
But Justice Incerti accepted Curtis had a troubled and depraved upbringing, tainted by abuse, violence and drug use.
His diagnosed complex post-traumatic stress disorder, depression and cannabis dependence reduced his moral culpability and would make his time in custody more difficult, the judge accepted.
Curtis also pleaded guilty at the earliest opportunity, which showed remorse and warranted a discount on sentence, Justice Incerti said.
Curtis was jailed for 24 years.
He will be eligible for parole after 17 years.
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