The little boy was born in London in the Lindo wing of St Mary's Hospital in Paddington, London - the same hospital where William and his brother Harry were delivered.
Reports suggest the baby was born at 4.24pm local time and weighed in at eight pounds and six ounces.
The new baby is third in line to the British throne after William, who was at his wife's side throughout the delivery, and his father Charles, Prince of Wales.
The newborn shares a birthday with Willem Dafoe, Selena Gomez, Don Henley and fashion designer Oscar de la Renta.
Further details, including the name of the child, have not been announced.
In line with tradition, a declaration of the baby's birth will be pinned up on a board outside Queen Elizabeth Ii's London residence, Buckingham Palace.