The baby weighs 8lbs 7oz.
The Duke of Cambridge was present for the birth. Her Royal Highness and her child are both doing well.
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.
Prince George and Princess Charlotte arrived at St Mary’s to meet their little brother after school with Prince William.
Her Royal Highness The Duchess of Cambridge has left St. Mary’s Hospital and The Duke and Duchess of Cambridge and their son travelled home to Kensington Palace, just seven hours after giving birth.
As the couple left, the Duke told reporters he was “very happy, very delighted, thank you”.
The baby is fifth in line to the throne and the Queen and the Duke of Edinburgh’s sixth great-grandchild.
In a statement, Kensington Palace said: “Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have received. “They would also like to thank everyone for their warm wishes.”