The couple, who welcomed a baby boy weighing 8lbs 7oz at 11.01am on 23 April, introduced their son to the world, standing on the steps of the Lindo Wing.
The proud parents beamed with happiness as they waved to the crowds, who had been waiting outside the hospital for up to 15 days to see the third royal baby.
The tiny fingers of their son could be seen moving as the couple looked around smiling at the crowds. The Duchess looked radiant wearing a red Jenny Packham dress with a contrasting white collar.
Kensington Palace tweeted a photo of the Duke and Duchess with their third child with the caption: “Welcome to the family.”
The couple went back into the Lindo Wing and emerged several minutes later carrying the unnamed prince in a car seat. William placed him in the rear of the car with Kate and then drove them away under police escort to Kensington Palace.
As he left, the Duke told reporters he was “very happy, very delighted, thank you”. He added: “Thrice the worry now.”
And to reporters, he said: “We didn’t keep you waiting too long this time.”
The palace said William will be “concentrating on his family” for the next couple of weeks.
Following the announcement of the third royal baby, a framed notice of the birth went on display on a ceremonial easel on the forecourt of Buckingham Palace. The notice reads: “Her Royal Highness the Duchess of Cambridge was safely delivered of a son at 11.01am today. Her Royal Highness and her child are both doing well.” It will remain in place for around 24 hours.
The Duchess’s labour was overseen by consultant obstetrician Guy Thorpe-Beeston, who is the surgeon-gynaecologist to the household, and consultant gynaecologist Alan Farthing, the Queen’s surgeon-gynaecologist – part of the team who delivered George and Charlotte.
Kensington Palace said the name of the baby would be announced in due course. Arthur, Albert and Philip are all thought to be in the running for the new royal baby’s name. Other suggested names include Frederick, Charles, James and Michael.
Kensington Palace confirmed Kate Middleton was in early stages of labour and admitted to the Lindo Wing at St Mary’s hospital on the morning of 23 April. It was understood she was taken to the private maternity unit before 6am.
The world’s press set up outside the Lindo Wing at the London hospital, waiting for the moment the couple introduced their new addition to the world. Kensington Palace tweeted a photo of the media gathered outside the private maternity unit.
The photo call on the steps of St Mary’s has become something of a family tradition as both Prince George and Princes Charlotte were also pictured in their parents’ arms in the very same spot shortly after their births.
A day after the birth of Prince George at 4.24pm on 22 July 2013, the family answered questions while the world’s press snapped the first photos of the newborn.
Prince William said he felt “very emotional,” and the Duchess said: “It’s very emotional and such a special time and I think any parent will probably know what this feeling feels like.”
The Duchess left hospital with Princess Charlotte on the same day she was born: 2 May 2015.
The baby’s father Prince William was also photographed in the same spot shortly after he was born in 1982.
The Duke and Duchess of Cambridge’s third child will be the Queen and the Duke of Edinburgh’s sixth great-grandchild. Prince Harry has shifted down the line of succession to sixth place.
The Duke of York, who was born second in line, will move to seventh and Princesses Beatrice and Eugenie to eighth and ninth.