Keiryn Nisbet, 21, went into Ronnie Simpson's house in Armadale, West Lothian, on October 6 last year and attacked his victim, who walked with a crutch.
Nisbet, who had never met Mr Simpson, had earlier been ordered to leave a pub where he had been drinking nearby.
Mr Simpson's daughter found his body when she arrived at his house later that night. He had been the victim of a sustained and brutal assault and suffered serious head injuries.
The murder sparked a huge police investigation, with more than 40 officers involved in the inquiry. They examined 1000 hours of CCTV footage in a bid to find the 67-year-old's killer. Hundreds of houses were also visited by police.
Friends said Mr Simpson, a father of two, was an "unassuming guy who wouldn't hurt a fly".
Nisbet was later arrested and charged with murder. He was convicted yesterday after a trial at the High Court in Edinburgh.
Detective Chief Inspector Robert Cowper, who led the investigation, said: "While nothing can undo the pain and suffering Mr Simpson's loss has had on his family and the impact in the local community, I hope that today's verdict can allow the family to move forward from this ordeal.
"Mr Simpson was a well-known local and the attack within his own home was a callous act, which Keiryn Nisbet has never offered any explanation for."
Nisbet will be sentenced on October 11.