Kate, 31, gave birth to the future king at 4.24pm on Monday, 22 July, with Prince William by her side at the private Lindo Wing at St. Mary's Hospital in Paddington, London.
The new arrival weighed 8lbs 6oz and will go by the title Prince of Cambridge. His names have yet to be announced.
During a public engagement in Yorkshire today, Camilla told reporters: "Mother, son, father are all doing well and I think it's a wonderfully uplifting moment for the country."
Referring to her husband Prince Charles, the father of Prince William, she added: "It's very exciting and it's wonderful for the grandfather. He is brilliant with children, so he'll have a wonderful time."
Charles added he is "thrilled and excited".
Prince Charles issued a statement yesterday evening on behalf of himself and Camilla, saying: "Both my wife and I are overjoyed at the arrival of my first grandchild. It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy.
"Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."
It's thought we will get our first glimpse of the royal baby today as Kate's hairdresser arrived at the hospital just after 10am, sparking speculation their departure is imminent.
So far the only public comment from the couple has been a short statement issued by Kensington Palace saying the new parents "couldn't be happier".
Stars congratulate Kate and William on their arrival:
Copyright: Dave Bedrosian/Future Image/WENN.com