In the handwritten letter, he said he and wife Catherine were "shocked" to hear of the death of Jacintha Saldanha and "have been thinking about her a lot." She and her nursing colleagues had looked after the Royal couple "extremely well", he said.
Ms Saldanha put a hoax phone call through to another staff member who revealed details of the Duchess of Cambridge's condition while being treated for severe morning sickness during her first pregnancy with Prince George.
2DayFM radio presenters, Mike Christian and Mel Greig, had pretended to be the Queen and Prince Charles to get put through in a stunt that went viral and was broadcast around the world.
Ms Saldanha, a married mother of two, was found dead aged 46 in her nursing accommodating near King Edward VII Hospital in London a few days later. She was said to have been humiliated and left three suicide notes, one of which held the DJs responsible for her death and suggested they pay her mortgage.
Her family spoke publicly for the first time, telling of their anger and inability to forgive the radio station, in an interview published in the UK's The Mail on Sunday newspaper at the weekend.
Her widower Ben Barboza said the letter from Prince William, which is dated 1st January, 2013, three weeks after his wife's suicide, was "so precious" as his family inevitably thinks of Ms Saldanha whenever they see Prince George or his parents.
In the letter, Prince William says, "It is unbelievably sad and we both extend to you and your family our deepest condolences. It must be a very difficult time for you all with many questions and thoughts, but we both pray that things will get easier for you… Many of the nurses in the hospital spoke highly of her and I'm sure you know how great a nurse she was."
Ms Saldanha's son Junal, 18, told how he had contemplated suicide himself as he struggled after losing his mother. Her adopted daughter Lisha, 17, hopes to study medicine in her mum's honour.
Sarah, Duchess of York, and her daughters Beatrice and Eugenie, sent a letter of condolences to Lisha, the family revealed. It said, "I send so much love for your broken heart. I am so sorry you are without your mummy. I lost mine in a car crash, and it is so final, and you wish you had said goodbye and said so much."
CONTENTS OF FULL LETTER FROM PRINCE WILLIAM:
Dear Mr Barboza,
I just wanted to write on behalf of Catherine and myself to say how sorry we were to hear about Jacintha.
It is unbelievably sad and we both extend to you and your family our deepest condolences. It must be a very difficult time for you all with many questions and thoughts, but we both pray that things will get easier for you.
'We were both very shocked to hear about Jacintha and have been thinking about her a lot recently. Many of the nurses in the hospital spoke highly of her and I'm sure you know how great a nurse she was.
Jacintha, and her colleagues, looked after us both extremely well, and I am just so sorry that someone who cared for others so much found themselves in such a desperate situation.
This letter comes with my thoughts and prayers to you all.
With my condolences,
If you or somebody you know is struggling with mental health issues please contact Lifeline for help and support.