Jacintha Saldanha, 46, was found dead on Friday, three days after she took a hoax call from two Australian radio station DJs that gave away medical details of Kate, the Duchess of Cambridge.
"I'm sure the whole House and indeed the whole country will join me in paying tribute to this nurse and giving all our sympathies and condolences to her family," Cameron told the House of Commons during Prime Minister's Questions.
She clearly loved her job, loved her work and cared deeply about the health of her patients and what has happened is a complete tragedy, he said.
"There will be many lessons that need to be learnt."
He also urged the press to keep their distance to allow Saldanha's family the time and space to grieve.
Saldanha had answered the Australian presenters' call in the early hours of the morning on December 4 and, believing they were members of the Royal Family, put them through to another nurse, who gave an update on the duchess's condition in detail.
The duchess was being treated in the King Edward VII's Hospital for hyperemesis gravidarum, an extreme form of morning sickness.
The result of a post-mortem examination on the nurse will be released at the inquest into her death tomorrow, Scotland Yard has said.
The examination to establish the cause of Saldanha's death began on Monday and has concluded but its result will not be officially announced until the hearing at Westminster Coroner's Court.
The death is not being treated as suspicious and the inquest is expected to be opened and adjourned as inquiries are continuing, BBC reported.
London: Describing the death of an Indian- origin nurse as a "complete tragedy", British Prime Minister David Cameron on Wednesday said "lessons need to be learnt" from the incident.
First Published: Wednesday, December 12, 2012, 22:17