Julia Martha Thomas, a wealthy widow aged 55, was killed by her 29-year-old housekeeper Kate Webster very close to Park Road in well-to-do Richmond, but her head was never found.
The case became known as the 'Barnes Mystery', which gripped London at the time.
Webster, a convicted thief and fraudster, chopped up Thomas with an axe, boiled the remains and gave the dripping to local children to eat.
A box containing human flesh was found in the nearby River Thames days after the killing and one of the victim's feet was found on an allotment.
Webster was tried and executed, but the head was never found until it was unearthed in October by workmen building an extension at the home of Attenborough, the face of BBC natural history programmes for more than 50 years.
Thomas lived at almost exactly the same spot as the 85-year-old broadcaster, while the garden where the skull was found used to be the site of a pub said to be a favourite of the killer.
Alison Thompson, the west London coroner formerly identified the recovered skull as that Thomas. She recorded a verdict of unlawful killing and the cause of death as asphyxiation and head injury.
After reviewing records of the murder from the time of her death, along with census records and radiocarbon testing, the investigating officer was able to provide the coroner with compelling evidence that the skull was indeed Thomas's.
"This is a fascinating case and a good example of how good old-fashioned detective work, historical records and technological advances came together to solve the 'Barnes mystery'," said Richmond borough police commander Chief Superintendent Clive Chalk.