Kate, the wife of Britain's Prince William, was admitted to hospital in the early stages of labour early on Saturday, Kensington Palace said.
The Duchess of Cambridge was taken to the private Lindow wing of St Mary's Hospital, West London by car, accompanied by Prince William at around 6 a.m. (0500 GMT), the palace added.
The new baby will be fourth-in-line to the throne, behind brother George, father William and grandfather Prince Charles.
William was born at the same hospital to the late Princess Diana in 1982.
The baby's gender is not known but bookmakers are tipping the child to be a girl, with Alice, Elizabeth, Charlotte and Victoria the favourite names. James and Arthur are the favourite boy's names.
In keeping with tradition, the official announcement of the birth will be made by placing a notice on an easel at the forecourt of Buckingham Palace.
