With the Royal baby having been introduced to the world, plans are in motion around the country for ceremonial traditions that accompany Royal births.
The couple’s second son, who was born at 11:01 BST, weighing 8lb 7oz, is fifth in line to the throne.
Prince George and Princess Charlotte had visited their brother at the Lindo Wing of St Mary’s Hospital, London.
Leaving the hospital Prince William said the couple were very happy, before holding up three fingers and joking he had “thrice the worry now”.
“We didn’t keep you waiting too long this time,” he added.
When someone asked him whether the couple had decided on a name, he said: “You’ll find out soon enough.”
Minutes earlier, Prince William and Catherine had come out of the hospital briefly to greet the crowds with their new son.
They then returned inside to put their newborn son in his car seat before driving away towards their home Kensington Palace.
Kensington Palace said the name of the baby would be announced in due course while a formal notice of the birth had been posted on the forecourt of Buckingham Palace.
Favourite names at the bookmakers include Arthur, Albert, Frederick, James and Philip.