Kate, the wife of Britain’s Prince William, was admitted to hospital in the early stages of labor early on Saturday, Kensington Palace said.
The Duchess of Cambridge was taken to the private Lindo wing of St Mary’s Hospital, West London by car, accompanied by Prince William at 6am (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 favorite names. James and Arthur are the favorite 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.
Kate, 33, and William, 32, met as students at St Andrews University in Scotland, married in a spectacular ceremony at Westminster Abbey in April 2011 and have since become global stars.
When Kate leaves hospital after giving birth, the couple will initially return to their London residence, Kensington Palace, for a couple of days, before heading to Anmer Hall, their country mansion on the queen’s Sandringham estate in Norfolk, to the northeast of London.
“The duke is working in East Anglia so the duchess may spend some time in Anmer but Kensington Palace will remain their primary residence,” a spokeswoman said.