Kate, 42, wife of heir-to-the-throne Prince William, had major abdominal surgery in January which revealed the presence of cancer and has been undergoing treatment since then.
In a personal message accompanying an intimate video of her with her husband and their three young children, Princess Charlotte, 9, and Princes George, 11, and Louis, 6, Kate said she would be carrying out a handful of public engagements later this year.
But she cautioned her path to full recovery would be long, and her focus was to remain cancer free.
"As the summer comes to an end, I cannot tell you what a relief it is to have finally completed my chemotherapy treatment," she said in her message.
"The last nine months have been incredibly tough for us as a family. Life as you know it can change in an instant and we have had to find a way to navigate the stormy waters and road unknown."
Kate spent two weeks in hospital in January after having surgery, and two months later she announced in a video message that tests had revealed the presence of cancer.
Her office, Kensington Palace, has declined to give any further details about the type of cancer or other specifics about her treatment, other than to say the preventative chemotherapy began in February.
She made her first public appearance this year in June at the annual military parade to mark the official birthday of King Charles, and then attended the Wimbledon tennis championships.
'SCARY'
"The cancer journey is complex, scary and unpredictable for everyone, especially those closest to you," she said.
"With humility, it also brings you face to face with your own vulnerabilities in a way you have never considered before, and with that, a new perspective on everything.
"This time has above all reminded William and me to reflect and be grateful for the simple yet important things in life, which so many of us often take for granted. Of simply loving and being loved."
King Charles, 75, who has also been undergoing treatment for cancer, and his wife Camilla consider Kate's announcement on Monday "wonderful news", a Buckingham Palace spokesperson said.
They will continue to offer all love, thoughts and support to the princess on her continued path to full recovery, the spokesperson added.
In the video, which was filmed last month in Norfolk, eastern England, the princess looked well and healthy.
The film showed the family walking through fields and woods, carrying a cricket bat and ball, and Kate holding hands with William and lying entwined together on a beach. In other footage she was shown pushing Louis on a swing and being joined by her parents as they played a card game.
She and William were grateful for the global messages of support, she said, adding she was looking forward to returning to public duties when she was able, although her programme for the remainder of the year will remain light.
"Doing what I can to stay cancer free is now my focus. Although I have finished chemotherapy, my path to healing and full recovery is long and I must continue to take each day as it comes," said the princess, often referred to by her maiden name Kate Middleton.
"Despite all that has gone before, I enter this new phase of recovery with a renewed sense of hope and appreciation of life ... To all those who are continuing their own cancer journey – I remain with you, side by side, hand in hand. Out of darkness, can come light, so let that light shine bright."
