Palace officials say Prince William's wife, Kate, has been admitted to the hospital in the early stages of labor.
In a brief statement, Kensington Palace said: "Her Royal Highness the Duchess of Cambridge has been admitted this morning to St Mary's hospital, Paddington, London, in the early stages of labour.
"The duchess travelled by car from Kensington Palace to the Lindo wing at St Mary's hospital with the Duke of Cambridge."
The duchess is expected to give birth in the private wing, where Princess Diana gave birth to William and his younger brother, Prince Harry.
The baby will be third in line for the British throne - behind Princes Charles and William - and is anticipated eventually to become king or queen.