Kate, 42, the wife of heir to the throne Prince William, spent two weeks in hospital in January after undergoing what her office said at the time was successful, planned surgery for an unspecified but non-cancerous condition.
However, in a video message, Kate, dressed in jeans and a jumper and looking pale and tired, 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."
The news is the latest major health blow for the British royal family after King Charles revealed in February that he too was to have treatment for cancer, meaning he has had to postpone his public royal duties.
After her operation, the palace said the princess, still popularly known by her maiden name Kate Middleton, would not return to official duties until after Easter, which falls at the end of this month. But her absence from public life has provoked intense speculation and wild rumours on social media.
She and William had wanted privacy about the cancer until their children, Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5, 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 ok," 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."
British 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.
"She has shown tremendous bravery with her statement today. In recent weeks she has been subjected to intense scrutiny and has been unfairly treated by certain sections of the media around the world and on social media."
As Kate Middleton, she was the first commoner to marry a marry a prince in close proximity to the throne in more than 350 years when she wed William in 2011 and has since become one of the most popular royals.
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.
