Barry Rogers and his mother Penny John were convicted this afternoon of murdering 84 year Betty Guy at her home in Johnston.
They were told immediately that at the sentencing hearing on Thursday morning they will receive life sentences.
The only question to be decided, said the judge, was the minimum number of years they must spend in jail before being allowed to apply for parole.
Rogers, aged 33, held his head in his hands and wept after the jury forewoman announced the unanimous verdicts.
John, aged 50, sat stoney faced and showed no emotion.
John was remanded in custody until the sentencing hearing. Rogers has been in custody throughout the trial at Swansea crown court.
The judge, Mr Justice Lewis, praised the jury for carrying out their duty "magnificently" and described the case as having been emotional and complex.
He said he would study sentences passed by other judges for mercy killings before deciding on the minimum terms.
He will also listen to pleas of mitigation by the couple's barristers.
Rogers and John killed Mrs Guy - his grandmother and her mother-because she was too old and suffered from ill health.
John mixed sedatives - including her own sleeping tablets - with whiskey and gave the mixture to her mother in the early hours of November 7, 2011.
That failed to kill her and Rogers, a former soldier, "finished her off" by placing a pillow over her face.
At first her death was believed to have been from natural causes and Mrs Guy's body was cremated at Narberth just four days later.
But Rogers could not keep his mouth shut and over the coming years told various women, including his one time wife, that he and his mother had killed her.
After they had been arrested detectives devised a clever plan to trap them.
Although they were living at different addresses police agreed to grant them bail as long as they both stayed at John's home in Maes Dre, Union Terrace, St Dogmaels.
Officers drove them to the address to make sure they abided by the bail conditions.
By then a listening device had been placed in the property- and as soon as they walked through the door they began talking about what they had done.
It was five years after they had killed Mrs Guy and neither could remember if they had swapped mobile telephone text messages that the police might be able to retrieve.
Rogers became worried his mother was "starting to crack" and urged her to stick to their story that Mrs Guy had died from old age.
But the jury saw through it.
John's reaction to the verdicts - or lack of it - surprised some in the court room.
She had been so worried by having to enter the witness box and answer questions that she needed several days of medication before she could face up to it.
But when the guilty verdict was announced there were no tears and she continued to stare straight ahead.
And when the judge sent her to jail to await sentencing she turned smartly and walked away with the dock officer.
Rogers, by contrast, rocked backwards and forwards with his head in his hands and sobbed. He tried to make contact with someone in the public gallery but with no apparent success before being led away.
After the verdict, Mrs Guy's daughter Lorraine Matthews said her family had been "shocked and horrified" to learn that her mother may have been murdered.
In a statement released through Dyfed-Powys Police, she said: "Seven years after my mother's death, my brothers, my sons, myself and other members of the family, were shocked and horrified to learn from the police that my mother, Mrs Betty Guy, may not have died from natural causes and that my sister and her son were to be charged with her murder.
"Over the past three years the police have worked tirelessly to collect sufficient evidence to bring this case to court.
"Now that the case has drawn to a close we are satisfied that justice has prevailed and now we can close this very sad chapter in our lives.
"All our thanks and gratitude go to Dyfed-Powys Police and the associated legal services in pursuing this case and bringing it to a successful conclusion."
Speaking after the verdict, Gemma Vincent, from the CPS, said : "Covert recordings such as these are not common.
"In this case it provided compelling evidence for the CPS to present to the jury, demonstrating that the killing of Betty Guy was deliberate and planned.
"Mrs Guy's life was cut short by her own daughter and grandson - our thoughts and sympathies are with those affected."
Chief inspector Steve Davies, from Dyfed Powys Police, said the investigation into Mrs Guy's death had been a protracted one and he wanted to thank her family for their support and cooperation during this "extremely difficult time".
"Today's guilty verdict provides some justice to the family who now wish to move on with their lives," he added.
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