Kate, the Princess of Wales, says she is undergoing preventative chemotherapy after tests taken following major abdominal surgery in January revealed that cancer had been present.
Kate, 42, the wife of heir-to-the-throne Prince William, spent two weeks in hospital in January after having what her office said at the time was successful, planned surgery for an unspecified but non-cancerous condition.
However, in a video message, Kate said subsequent tests had revealed cancer had been found.
She said she was well and getting stronger.
"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," Kate said in the video which was filmed on Wednesday.
"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."
King Charles revealed in February that he too was to have treatment for cancer, meaning he has had to postpone his public royal duties.
Buckingham Palace said on Friday that the King is proud of Kate for her courage in speaking about her treatment.
Charles is "so proud of Catherine for her courage in speaking as she did" and has "remained in the closest contact with his beloved daughter-in-law throughout the past weeks," after they spent time in hospital together, a Buckingham Palace representative said.
Charles and his wife Camilla "will continue to offer their love and support to the whole family through this difficult time," the spokesperson added.
Kate's office, Kensington Palace, said it would give no further details about the type of cancer.
It said she was on a recovery pathway and the preventative chemotherapy had begun in February.
After her operation, the palace said Kate would not return to official duties until after Easter but her absence from public life has provoked intense speculation on social media.
She and William had wanted privacy about the cancer until their children, Prince George, 10, Princess Charlotte, eight, and Prince Louis, five, began their school holidays which started on Friday.
"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 okay," she said.
"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."
Kate has not appeared at a public event since she joined other members of the royal family for a church service on Christmas Day.
However, a video filmed last Saturday by a member of the public which was published by the Sun newspaper showed Kate looking healthy, walking and carrying shopping bags alongside her husband at a farm shop in Windsor, near to their home.
"We hope that you will understand that, as a family, we now need some time, space and privacy while I complete my treatment," Kate said.
"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."
United Kingdom Prime Minister Rishi Sunak said Kate should be afforded the privacy to focus on her treatment and be with her family.
"The Princess of Wales has the love and support of the whole country as she continues her recovery," Sunak said in a statement.
Kensington Palace said William would continue his duties while supporting his wife, as he had since her surgery.
A source said Kate was in good spirits and focused on her 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," Kate said.
