The baby weighed 8lbs 6oz and was born at 4.24 p.m., the palace said.
"Her Royal Highness and her child are both doing well and will remain in hospital overnight," Kensington Palace said in a statement.
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.
The official notice of birth has left St Mary's Hospital and is making its way towards Buckingham Palace.
The new royal baby is third in line to the throne and a future king. A great-grandchild to the Queen – her third – the newborn will also one day be crowned sovereign.
If the baby follows after the Prince of Wales and the Duke of Cambridge as king, he will be the 43rd monarch since William the Conqueror obtained the crown of England.
The baby's uncle, Prince Harry, now moves to fourth in line to the throne, while the Duke of York shifts down to fifth and Princesses Beatrice and Eugenie to sixth and seventh place.
More to follow...