His Majesty revealed his diagnosis in February and is still receiving outpatient care for his illness.
The King is to return to public-facing royal duties, with his medical team “very encouraged” by the progress made in his cancer treatment.
The monarch has been receiving outpatient care since early February and despite the good news, palace sources stressed His Majesty is still continuing treatment.
The announcement that the King is doing well will be a morale boost for the family, with both him and the Princess of Wales being diagnosed with cancer.
A Buckingham Palace spokesperson said: “His Majesty’s medical team are very encouraged by the progress made so far and remain positive about the King’s continued recovery.”
They added: “His Majesty’s treatment programme will continue, but doctors are sufficiently pleased with the progress made so far that the King is now able to resume a number of public-facing duties.”
The palace also released a new photograph of the King and Queen, taken in Buckingham Palace on 10 April, the day after their 19th wedding anniversary.
To mark his full return, Buckingham Palace said the royal couple will visit a cancer treatment centre on Tuesday.
“This visit will be the first in a number of external engagements His Majesty will undertake in the weeks ahead,” the palace said.
“In addition, The King and Queen will host Their Majesties The Emperor and Empress of Japan for a state visit in June.”
The King and Queen are to celebrate the first anniversary of their coronation on 6 May.
The palace said: “Their Majesties remain deeply grateful for the many kindnesses and good wishes they have received from around the world throughout the joys and challenges of the past year.”
The prime minister has welcomed the news, posting on X: “Brilliant news to end the week!”