The Duke and Duchess of Cambridge said in a statement they were “deeply saddened” by the death of the nurse, named as Jacintha Saldanha.
King Edward VII hospital paid tribute to “a first class nurse” who was the “victim of a hoax call.”
Details of the pregnant duchess’s medical condition were unwittingly revealed to two Australian DJs.
The DJs, from Sydney radio station 2Day FM – which says it is preparing a statement – posed as the Queen and Prince Charles.
The duchess had been admitted on Monday for acute morning sickness, and was discharged on Thursday.
‘Excellent nurse’
BBC royal correspondent Peter Hunt said he understood Mrs Saldanha was the person who answered the call from the Australian DJs and was not the nurse who discussed the duchess’s medical condition.
Mrs Saldanha, a duty nurse, answered the telephone because it was 05:30 GMT in the morning and there was no receptionist on duty.
The BBC understands Mrs Saldanha had not been suspended or disciplined by the hospital.
The St James’s Palace statement said the duke and duchess “were looked after so wonderfully well at all times by everybody at King Edward VII Hospital, and their thoughts and prayers are with Jacintha Saldanha’s family, friends and colleagues at this very sad time”.
A palace spokesman later added that “at no point did the palace complain to the hospital about the incident”.
“On the contrary, we offered our full and heartfelt support to the nurses involved and hospital staff at all times.”
In a statement outside the hospital, King Edward VII chief executive John Lofthouse said: “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.”
He added: “Jacintha has worked at the King Edward VII’s Hospital for more than four years.
“She was an excellent nurse and well-respected and popular with all of her colleagues.”
Scotland Yard said officers were called at 09:35 GMT on Friday after reports of a woman found unconscious at an address in central London.
They said the death is not being treated as suspicious.
Source: BBC News Online