The former Manchester United player's son Alex posted the news of his grandfather's passing on Twitter and asked for his family's privacy to be respected.
"Unfortunately my grandad passed away this morning, it's been a terrible few days as my gran was taken seriously ill last Monday and is in hospital," he wrote.
"My dad is in need of a few days to get over this shock and I hope his privacy is respected at this tough time. Thanks."
Bruce is currently caring for his mother Sheenagh, who took ill on the eve of Villa's victory over Sheffield United in the Championship last weekend.