The Duchess and her mother, Doria Ragland, will be staying with the family at Frogmore Cottage.
The 33-year-old royal confirmed the arrival of his son on Monday afternoon UK time.
"I haven't been at many births,” he said. “This is definitely my first birth - it was amazing, absolutely incredible. I'm so incredibly proud of my wife. And as every father and parent would say, your baby is absolutely amazing. But this little thing is absolutely to-die-for so I'm absolutely over the moon."
The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, The Duke and Duchess of Cambridge, Lady Jane Fellowes, Lady Sarah McCorquodale and Earl Spencer were said to be "delighted with the news", the palace said.
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