Jacintha Saldanha, a nurse at King Edward VII Hospital in central London, is believed to have answered the call from two Australian DJs, and transferred them to Kate's nurse.
Ms Saldanha was found dead at an address close to the hospital this morning. It is reported that she took the phone call because it was during the night, when there was not a receptionist on duty.
Two Australian DJs, Mel Greig and Michael Christian, from radio show 2Day FM, called the hospital earlier this week pretending to be members of the Royal family. They played their conversation with Kate's nurse out live on their show.
The hospital announced the news with 'very deep sadness', saying:
"It is with very deep sadness that we confirm the tragic death of a member of our nursing staff, Jacintha Saldanha.
"Jacintha has worked at the King Edward VII Hospital for more than four years. She was an excellent nurse and well-respected and popular with all of her colleagues.
"We can confirm that Jacintha was recently the victim of a hoax call to the hospital. The hospital had been supporting her throughout this difficult time."
St James's Palace did not make a complaint against the hospital after the prank call.
In a statement, the Metropolitan Police said: "Police were called at approx 0935hrs on Friday, 7 December, to reports of a woman found unconscious at an address in Weymouth Street, W1.
"LAS attended and the woman was pronounced dead at the scene. Inquiries continue to establish the circumstances of the incident. Next of kin have been informed. The death is being treated as unexplained."