Former Para Kane, 41, was found guilty of killing Kathleen Milward at her home at Brodie Place, Stonehouse, Lanarkshire, on January 3. The jury took just three hours to find him guilty by majority.
Judge Lord Matthews will determine how many years Kane must serve behind bars before being eligible for parole when he sentences him in January.
As the verdict was given, Kane turned round and glared at his aunt Maureen Kennedy who sat sobbing in the public gallery at the High Court in Dumbarton.
His mother, Kathleen Kane, sat weeping on the other side of the court from her sister.
Outside the court, Maureen Kennedy said: "I don't hate my nephew, but I hate what he has done."
She laid the blame for the killing on Kane's addiction to heroin.
Jennifer Bain, prosecuting, told the court that Kane has previous convictions for breach of the peace and theft and was jailed for four months at Winchester Crown Court in 1997 for actual bodily harm.
At the time of the murder, he had been on bail from Hamilton Sheriff Court.
Kane bludgeoned his frail gran, who suffered from heart problems and high blood pressure, to death, and then phoned his drug dealer to buy heroin.
He left the woman who had helped bring him up and who regarded him as a son, dead or dying on her kitchen floor and went off to smoke heroin.
Hours later when he returned, he pretended to find her body and claimed he knew nothing about her horrific injuries.
But he was snared by forensic evidence on his clothing and on his gran which proved that he was the killer.
Judge Lord Matthews told Kane: "The jury have found you guilty of a charge of murder. The only sentence I can impose is one of life imprisonment."
Sentence was deferred for reports.
After the verdict, Maureen Kennedy said: "I believe that ultimately drugs, namely heroin, killed my mother. Drugs are a curse on society.
"Garry Kane is an addict. His life became a daily struggle to get from one fix to the next.
"He has caused unspeakable and unbearable pain to all his family. Justice has been done, but there are no winners and it won't bring my mother back."