Prince Louis Arthur Charles, the couple's third child, who joins brother George, 4, and sister Charlotte, 2, and becomes fifth-in-line to the throne, was born on Monday last week, weighing in at 8 lbs 7oz.
On Tuesday, William and Kate, formally known as the Duke and Duchess of Cambridge, signed the birth register at their Kensington Palace home in central London in front of an official from Westminster Register Office.
All newborns in Britain have to be registered, with details of the parents and their occupation. William and Kate duly listed their jobs as Prince and Princess of the United Kingdom.