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Catherine, the Princess of Wales, is undergoing chemotherapy treatment for cancer.
The wife of Prince William, the heir to the British throne, made the announcement in a personal video message released by Kensington Palace at 6pm on Friday (5am on Saturday AEDT).
Kate, 42, started her message by thanking the support she has had during "an incredibly tough couple of months for our entire family".
FULL STATEMENT: Kate thanks public, says she is 'getting stronger every day'
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She said her abdominal surgery was not thought to be cancerous but tests later found cancer had been present.
"My medical team therefore advised that I should undergo a course of preventative chemotherapy and I am now in the early stages of that treatment."
She said it had been "a huge shock" for her and William and has taken time for her to recover from major surgery in order to start the cancer treatment.
"But, most importantly, it has taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be OK," she said.
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"As I have said to them; I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirits.
"Having William by my side is a great source of comfort and reassurance too. As is the love, support and kindness that has been shown by so many of you. It means so much to us both."
Kate asked for "some time, space and privacy" while she completes her treatment.
"My work has always brought me a deep sense of joy and I look forward to being back when I am able, but for now I must focus on making a full recovery.
"At this time, I am also thinking of all those whose lives have been affected by cancer. For everyone facing this disease, in whatever form, please do not lose faith or hope. You are not alone."
Buckingham Palace has released a statement saying King Charles III is "so proud" of his "beloved" daughter-in-law.
The monarch, who is undergoing his own cancer treatment, has remained in "closest contact" with Catherine in recent weeks.
The King was admitted to the London Clinic, at the same time as his daughter-in-law, for prostate treatment and Buckingham Palace announced on February 5 that the monarch had been diagnosed with cancer.
Similarly to Kate's situation, the palace has not elaborated on what type of cancer Charles is being treated for.
Timeline of events
There has been widespread speculation about the future queen who has been missing from public life since undergoing abdominal surgery at the London Clinic on January 16.
She was last seen on public duty at a Christmas service in Sandringham alongside William and their three children: Prince George, 10, a future king, Princess Charlotte, 8, and Prince Louis, 5.
The palace announced Kate's abdominal surgery but did not elaborate, except to say she was not expected to return to public duties until after Easter.
Rumours and conspiracy theories have grown over the many weeks Kate has been out of the spotlight, culminating on March 10, Mother's Day in the UK, when a photo released by the royal family of the princess with her three children turned out to be heavily edited.
The photo, the first official one since Kate underwent surgery, was recalled by major news agencies that determined it had been digitally manipulated.
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The princess released an apology the next day for "confusion" caused by the photo, saying that like many amateur photographs she "occasionally experiments with editing".
The Sun newspaper next published a video reportedly of Kate and William shopping in Windsor on March 16. Sources inside the palace told media they hoped the footage would put conspiracies and rumours to bed.
Kate's full statement
"I wanted to take this opportunity to say thank you, personally, for all the wonderful messages of support and for your understanding whilst I have been recovering from surgery," Kate said in her statement.
"It has been an incredibly tough couple of months for our entire family, but I've had a fantastic medical team who have taken great care of me, for which I am so grateful.
"In January, I underwent major abdominal surgery in London and at the time, it was thought that my condition was non-cancerous. The surgery was successful. However, tests after the operation found cancer had been present. My medical team therefore advised that I should undergo a course of preventative chemotherapy and I am now in the early stages of that treatment.
"This of course came as a huge shock, and William and I have been doing everything we can to process and manage this privately for the sake of our young family.
"As you can imagine, this has taken time. It has taken me time to recover from major surgery in order to start my treatment. But, most importantly, it has taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be ok.
"As I have said to them; I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirits.
"Having William by my side is a great source of comfort and reassurance too. As is the love, support and kindness that has been shown by so many of you. It means so much to us both.
"We hope that you will understand that, as a family, we now need some time, space and privacy while I complete my treatment. My work has always brought me a deep sense of joy and I look forward to being back when I am able, but for now I must focus on making a full recovery.
"At this time, I am also thinking of all those whose lives have been affected by cancer. For everyone facing this disease, in whatever form, please do not lose faith or hope. You are not alone."
