Gladys Hooper from Ryde, Isle of Wight,had the surgery after falling and breaking her hip.
Her son, Derek Hermiston, 84, said the operation had gone "splendidly" and had given his mother a "new lease of life".
"I think she is the oldest person in the world to have a hip operation and the surgeon, Jason Millington, and the anaesthetist were both courageous to take the decision to operate on someone of that age but the operation went splendidly," he said.
He said, "She is standing but not walking yet, they are taking it rather carefully with her as you never know what happens at that age. She listens to music and she's chatting away".
Guinness World Records currently lists John Randall as the oldest person to have a total hip replacement at the age of 102 years, three months and 30 days at Pinderfields hospital in Wakefield, West Yorkshire, in November 2011.
Hooper was born in Dulwich, south-east London, and was brought up in Brighton, East Sussex, before she became a concert pianist, started one of the first hire-car companies and later ran Kingscliff House school, which went on to become Brighton College.
"I have had correspondence since the surgery to suggest that not only is Mrs Hooper the oldest patient in the UK to have had hip fracture surgery, but possibly the oldest documented case worldwide," he said.
"The risks of surgery, and just as important anaesthesia, therefore can be justified. Age, however is not a risk in itself but more a marker that the patient is likely to have significant other health problems. As this particular patient has even made it to the age she has, by definition her health is much better than average," he said.
