Prince William was present for the birth of their son who weighs 8lbs 7oz.
The statement from the Kensington Palace read, "Her Royal Highness and her child are both doing well".
The name of the baby will be announced in due course.
The couple already has two children - a son, Prince George, aged 6, and a daughter, Princess Charlotte, aged 2.
The new prince is the Queen's sixth great-grandchild.(ANI)