Joanne Hussey, 33, of Yeadon, repeatedly struck 77-year-old Annie Garbutt's chest and head with a spade – spattering blood on her bedroom walls.
Widow Mrs Garbutt owned her two-bedroom cottage in Mirfield, near Dewsbury, where the killing happened and had "not inconsiderable" savings.
Hussey was worried about the financial implications of Mrs Garbutt going into a home.
She admitted manslaughter on the grounds of diminished responsibility, but denied murder – claiming voices in her head told her to do it.
But after a two week trial, a Leeds Crown Court jury took just one hour to find her guilty of the murder on May 7 last year.
Hussey, from Yeadon, hung her head in the dock as Judge Scott Wolstenholme told her to expect a life sentence.
The judge adjourned sentencing until June 11 for psychiatric reports to be prepared.
Hussey was alleged to have asked her mother Maureen Hussey to offer a friend £1,000 in return for saying she knew about the voices she claimed told her to kill.
After the verdict, Detective Superintendent Andy Brennan said: "This was a particularly brutal and callous crime.
"Hussey went to great lengths to conceal her involvement in this crime by attempting to forensically clean her car, clothing, the scene and the spade used to kill Annie.
"However, due to some methodical and painstaking police work by the detectives who were dealing with Hussey and the team of scientists from the Forensic Science Service at Wetherby, Hussey's criminality soon became clear to those who were hunting for Annie Garbutt's killer.
"As the investigation developed, a clear picture emerged of Joanne Hussey.
"Firstly, she was an accomplished liar and for a number of days quite brazenly denied any involvement in her grandmother's death until all of the evidence became overwhelming clear to her that she had nowhere to turn.
"Secondly, she would stop at nothing to avoid being prosecuted and ultimately convicted, by attempting to get her family and friends to tell lies to the police on her behalf.
"It is my belief Annie Garbutt was brutally killed because Joanne Hussey was motivated by greed. Annie would still have been alive today had Joanne Hussey not been concerned about her grandmother's personal finances being used to ultimately look after her."
Annie''s brutal death was a tragic end to her life at the hands of her own granddaughter."