10:43 AM PT -- King Charles III has notified both of his sons -- Prince William and Prince Harry -- about his diagnosis ... and both of them are rushing to be by his side. Will is said to be in regular contact with his dad, and is obviously nearby to see him in person too.

As for Harry ... he's reported to be flying into the UK in the coming days to see his father.

Major health update out of Buckingham Palace ... King Charles III is fighting cancer.

Buckingham Palace – the United Kingdom's royal residence – released an official statement Monday saying ... "During The King’s recent hospital procedure for benign prostate enlargement, a separate issue of concern was noted. Subsequent diagnostic tests have identified a form of cancer."

The Palace adds ... "His Majesty has today commenced a schedule of regular treatments, during which time he has been advised by doctors to postpone public-facing duties."

Charles, the Palace says, will continue with his state business and official paperwork despite the diagnosis.

As we reported, Charles was admitted to a London hospital last month for a "corrective procedure" for an enlarged prostate. Kate Middleton was in the same hospital at the same time for stomach surgery.

The Palace says Charles "remains wholly positive about his treatment and looks forward to returning to full public duty as soon as possible."

The Royal family says it's announcing Charles' diagnosis "to prevent speculation and in the hope it may assist public understanding for all those around the world who are affected by cancer."

It's interesting ... Charles' cancer announcement comes on the heels of World Cancer Day.

The King's wife, Queen Camilla, last week opened a new cancer support center at Royal Free Hospital in the UK.