A jury at the Old Bailey found that Alexander Rawson, 63 , had attacked and killed Eileen Dean less than two weeks after he moved into the home in which she was living.
Police were called at around 12.40am on Monday, 4 January after Eileen was found in her bedroom with severe facial and head injuries.
Despite being taken to hospital, she died later the same day.
Detectives from the Met’s Specialist Crime Command launched an investigation and examined CCTV from the night of her death.
Although the bedrooms of Rawson and Eileen were out of shot, the footage showed him holding a metal walking stick and walking towards their bedrooms at around 10.20pm
He was next seen on camera coming from the same direction approximately two hours later. No-one else was captured on CCTV between that time period.
A heavily bloodstained metal walking stick, believed to have been used to inflict Eileen’s injuries, was found on her bed.
Rawson was unfit to stand trial and so the jury were asked to decide whether he did the act charged against him.
He will be sentenced on Monday, 20 December.
Detective Chief Inspector Chris Wood, who led the investigation, said: “Our thoughts remain with Eileen’s family who have been through an incredibly traumatic experience and conducted themselves with the utmost respect and dignity throughout this trial process.
“Eileen was a completely defenceless woman whose life was suddenly taken away in a horrific manner. She had already been through a great deal, losing her husband almost 30 years ago, but she was described as a calm, quiet and lovely woman by all those who knew her.
“We hope her children and grandchildren have the space to grieve together now the trial is complete and to remember Eileen for the wonderful woman she was.”