Princess Kate, the wife of Britain’s Prince William, was admitted to the hospital in the early stages of labour early on Saturday, Kensington Palace said.
The Duchess of Cambridge, 33, was taken to the private Lindo wing of St Mary’s Hospital, West London by car, accompanied by Prince William, the palace added.
The arrival of the baby is edging closer to Britain’s May 7 general election.
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 as 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.
Kate, 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 the 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 spokesperson said.
Prince Charles is hoping to cradle a granddaughter.
The prince was chatting with a 100-year-old veteran at Windsor Castle on Thursday when he brought up the royal baby. The veteran’s daughter, Lynda Bateman, said: “My father introduced me as his daughter and Prince Charles asked how many daughters he had.
“My father said ‘One - and that’s enough!’ and Charles laughed and said ‘We’re hoping for a granddaughter!’”
Dozens of journalists and avid royalists have been waiting for days outside St Mary’s Hospital.
As the ‘Great Wait for Kate,’ as it's been dubbed, drags on, bookmakers say speculation is mounting about the baby’s name.
“In the last 48 hours, everyone is saying the name is more likely to be Charlotte than Alice,” Rupert Adams of betting firm William Hill said on Friday.
“We can’t find a particularly good reason. But money talks, and when we see a rush of money like this, it’s often as a result of people actually knowing what they’re told.”
Jessica Bridge of Ladbrokes said: “Obviously the gender’s a 50:50 shot, but not as far as the money’s concerned. Punters betting with their heart are backing a girl, whereas savvy punters betting with their head reckon it’s a boy.”