Prince William today revealed how Princess Charlotte and Prince George are 'delighted' at the arrival of their little brother who was born at 11.01am.
William joked that he didn't keep world waiting for too long after she went into labour at around 6am before giving birth five hours later.
He said of the name of the new baby, who is now fifth in line to the throne: ‘You’ll find out soon!'
The beaming parents looked delighted as they showed off their third child to the world who was born weighing 8lbs 7oz on St George's Day.
Prince George and Princess Charlotte were taken to meet him in their school uniform nearly six hours after Kate gave birth.
William was present for the birth this morning, and both Kate and the child were 'doing well', according to a Kensington Palace spokesman. Other members of the royal family were all said to be 'delighted with the news'.
Kensington Palace said: 'Her Royal Highness The Duchess of Cambridge will be leaving St. Mary's Hospital this evening. The Duke and Duchess of Cambridge and their son will travel home to Kensington Palace.'
A statement added: 'Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have received.'
It is anticipated that the grandparents will meet their grandson at Kensington Palace tomorrow.
An easel with a bulletin announcing the royal birth was put on display outside Buckingham Palace.
The notice reads: 'Hey Royal Highness the Duchess of Cambridge was safely delivered of a son at 11.01am today. Hey Royal Highness and her child are both doing well.'
Kensington Palace said the name of the baby would be announced in due course.
Celebrities and politicians have been sending their best wishes to The Duke and Duchess of Cambridge on social media.
Prime Minister Theresa May sent her 'warmest congratulations to the Duke and Duchess of Cambridge on the birth of their baby boy.'
'I wish them great happiness for the future,' she added.
Princess Diana's brother Charles Spencer joined well-wishers by tweeting 'Very sweet!' alongside the photos of Prince George and Princess Charlotte going to visit their new baby brother.
Earlier, excitement was building outside St Mary's Hospital, where some fans had been camped out for 15 days hoping for a glimpse of the royal baby.
Today, press pens opened outside the hospital as journalists, photographers and camera crews waited for confirmation of the baby's arrival.
Although the Queen has four children, the duke is the first future king to have a third for more than 120 years.