Williamina Elizabeth Scott was crossing Market Square in Duns on foot at around 11.40am on Friday when she was struck by a blue Seat Ibiza car.
She was taken to the Edinburgh Royal Infirmary, where she later died from her injuries.
PC Peter Valentine from Police Scotland said: “I’d like to appeal to anyone who was in the area of Market Square, Duns at the time, and who may have witnessed this incident, to contact Police on 101.”