Prince George and Princess Charlotte have arrived at hospital to meet their new baby brother.
The new prince, who was born at St Mary's Hospital, London, at 11:01 BST, weighing 8lb 7oz, is fifth in line to the throne.
Before entering through the doors of the Lindo Wing, Charlotte turned to wave to the crowds.
Kensington Palace said the Duchess of Cambridge and her son, who is yet to be named, are "both doing well".
Members of both families had been informed and were "delighted with the news".
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.
Prime Minister Theresa May tweeted her "warmest congratulations" to William and Catherine.
She said: "I wish them great happiness for the future."
Labour Party leader Jeremy Corbyn also sent his regards, tweeting: "Congratulations to Kate and William on the birth of their baby boy. I wish them all the very best."
The Archbishop of Canterbury added: "Congratulations to The Duke and Duchess of Cambridge on the safe delivery of their baby, a brother for Prince George and Princess Charlotte.
"May God bless them and all of their children with love, happiness and health."
Mayor of London Sadiq Khan tweeted: "On behalf of Londoners, I want to send our warmest congratulations to the Duke & Duchess of Cambridge on the birth of their baby boy."
Sir Vince Cable, leader of the Liberal Democrats, said: "Congratulations to the Duke and Duchess of Cambridge on the birth of their son.
"I'm sure his older brother will be delighted he has been born on St George's Day!"