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."
(Pics : Dailymail)