The Duke and Duchess of Cambridge left the hospital after the arrival of their third child, a boy.
The new prince, who was born at St Mary's Hospital, London, at 11:01 BST, weighing 8lb 7oz, is the fifth in line to the throne.
Previously, Prince George and Princess Charlotte visited their younger brother at the Lindo Wing.
The Palace of Kensington said that the Duchess of Cambridge and her son, who still do not know each other, "both are fine".
Just before 18:00 BST, Prince William and Catherine left the hospital briefly to greet the crowd with their new son.
Then they went back inside to pick up the seat of their newborn son before leaving for Kensington Palace.
The members of both families had been informed and were "delighted with the news".
Kensington Palace said that the baby's name would be announced in due time, while a formal announcement of the birth had been posted on the Buckingham Palace esplanade.
The favorite names of bookmakers include Arthur, Albert, Frederick, James and Philip.
Prime Minister Theresa May he tweeted his "warmest congratulations" to William and Catherine.
She said: "I wish you great happiness for the future."
Labor Party leader Jeremy Corbyn also sent his greetings, tweeting: "Congratulations to Kate and William for the birth of their baby, I wish them well."
The Archbishop of Canterbury added: "Congratulations to The Duke and Duchess of Cambridge for the safe delivery of their baby, baby, brother of Prince George and Princess Charlotte.
" May God bless them and all their children with love, happiness and health. "
The mayor of London, Sadiq Khan, tweeted:" On behalf of the Londoners, I want to send our warmest congratulations to Duke & Duchess of Cambridge for the birth of her baby. "
Sir Vince Cable, leader of the Liberal Democrats, said: "Congratulations to the Dukes and Duchess of Cambridge for the birth of their baby." Son.
"I'm sure your older brother will be happy to have born on St. George's day! "
A sense of renewal
By Jonny Dymond, BBC's real correspondent
After a few more quiet times, the royal family is back in the news, and there is a remarkable sense of renewal new faces, with Meghan Markle, Prince Harry's fiancee, making her first public appearances, and now another child, the third son of Duke and Duchess of Cambridge, still unnamed.
It has always been like this – waves of interest followed by periods of relative tranquility. But there has been a sense of renewal in recent months.
Of course, there has been concern about the health of the Duke of Edinburgh; and the interest in the Queen, with her decades of service, never falters.
But the attention of a new group, both in Britain and around the world, has been caught by this birth and then the wedding of Prince Harry and Meghan Markle next month.
From the darkest days of World War II to the generation of Instagram, the Royal Family now connects them all.
Following a change in the law in 2013, Princess Charlotte remains in fourth place in the row of the throne.
Previously, the younger real men would have had priority over the older sisters.
The duchess was admitted to the hospital shortly before 06:00 on Monday with the announcement of the birth shortly after 1:00 p.m.
On the scene
By Kate Whannel, BBC News, outside St Mary's Hospital
Champagne corks burst and cheers were heard when news of the Duchess had given birth to a child running between the crowd.
Those who had been encamped for days led the chants: "He is a boy, he is a boy."
Others began to sing: "Congratulations and celebrations, it's a child born on St. George's Day".  Multimedia playback not supported on your device
Guy Thorpe-Beeston, obstetrician consultant to real doctors and gynecologist consultant Alan Farthing supervised the birth.
Both were summoned for the arrival of Prince George in 2013 and Princess Charlotte in 2015.
The new prince, born on St. George's day, shares a birthday with Lady Gabriella Windsor, the daughter of the Prince and the Princess Michael de Kent, who was born in Lindo Wing on April 23, 1981.
Will the new prince be the king?
Becoming King or Queen, since the third royal son is rare, and has not yet happened within the current House of Windsor.
But the third son of George III and Queen Charlotte, William IV, took over the task and ruled from 1830 to 1837.
The king of Hannover acceded to the throne at age 64 when his older brother, George IV, He died without an heir.
He became next when he was 62 years old and his other older brother, Frederick, Duke of York, died.
Have you, or anyone in your family, had a baby today? Send an email.
Include a contact number if you are willing to talk to a BBC reporter. You can also contact us in the following ways:
- WhatsApp: +44 7555 173285
- Send photos / videos to
- Upload your photos / videos here  Tweet: @BBC_HaveYourSay
- Send an SMS or MMS to 61124 or +44 7624 800 100