LONDON—Catherine, Princess of Wales, said Monday that she had completed her chemotherapy treatment and would resume a light program of royal duties in the coming months, a boost for the British royal family, which had been rocked by her surprise cancer diagnosis earlier this year.

In a video statement, Catherine said that she would resume duties as and when she is able and that she is feeling well and “looking to the future.” In March, Catherine, 42 years old, said that she had an unspecified type of cancer and that she was in the early stages of preventive chemotherapy.

Kensington Palace released a video Monday, filmed in the woods of Norfolk last month, showing a healthy-looking Catherine on a day out with her three children and husband Prince William.

“I cannot tell you what a relief it is to have finally completed my chemotherapy treatment,” she said. “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.”

Catherine is expected to undertake a handful of engagements over coming months, but she warned her journey to a full recovery is long. “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.”

Kensington Palace hasn’t said what cancer Catherine was diagnosed with or what stage it was. Nor has it confirmed which events she will turn up at. However, the palace has said she has already resumed working from home on her projects, including research into early-childhood years.

The film showed the princess sharing a picnic in a wood and jumping in and out of waves on the English coast with her husband, in one of the most intimate videos Kensington Palace has released of the family to date.

Write to Max Colchester at Max.Colchester@wsj.com