The Duchess of Cambridge has given birth to a son at the Lindo Wing of St Mary's hospital in London.
The baby is now the fifth in line to the British throne.
The royal baby weighs 8lbs 7oz (about 3.8kg).
The palace says the child was born at 11:01am (8pm Australian time), a few hours after Kate was admitted to London's St Mary's Hospital in labour.
Prince William was present for the birth of his son.
The palace says "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."
The new prince is Queen Elizabeth's sixth great-grandchild and fifth-in-line to the British throne behind siblings Prince George, 4, his two-year-old sister Princess Charlotte, their father William, and grandfather and heir Prince Charles.
A 2013 change to the law means the boy will not supplant older sister Charlotte in the line of succession.
"That would in fact be the first time that has ever happened," royal historian Huge Vickers said.
However, William's younger brother Harry, who marries US actress Meghan Markle next month, falls to sixth on the list.
Kensington Palace said the name of the new royal would be announced in due course.
Bookmakers had made Albert, Arthur, Jack and Fred the favourite names for a boy.
British Prime Minister Theresa May on Monday congratulated Prince William and his wife Kate on the birth of a boy.
"My warmest congratulations to the Duke and Duchess of Cambridge on the birth of their baby boy," May said.
"I wish them great happiness for the future."
More to come.
