Her husband Prince William was present as his wife gave birth to our future king, who is third in line to the throne.
Buckingham Palace said the Royal family are delighted with the news.
Buckingham Palace said the Royal family are delighted with the news.
A statement said: "Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 4.24pm. The baby weighs 8lbs 6oz.
"The Duke of Cambridge was present for the birth.
"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news.
"Her Royal Highness and her child are both doing well and will remain in hospital overnight."
A town crier announced the arrival of the baby outside the hospital and a notice giving details about the baby was transported by car to Buckingham Palace.
The notice was placed in an easel in the palace's forecourt, much like when Prince William was born on June 21 1982.
The notice was placed in an easel in the palace's forecourt, much like when Prince William was born on June 21 1982.
Prince Charles said he was "enormously proud and happy to be a grandfather for the first time", adding that it was "an incredibly special moment for William and Catherine".
He added: "Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."
While Prime Minister David Cameron spoke outside 10 Downing Street to say the birth of the royal baby was 'an important moment in the life of our nation.'
The Duke of Cambridge issued a short statement, saying: "We could not be happier."