An easel is placed in the forecourt of Buckingham Palace announcing the birth of a baby girl to Catherine, Duchess of Cambridge, in London, Britain May 2, 2015. [Photo/Agencies]

Party leaders tweeted their congratulations for the royal family.

"Congratulations to the Duke and Duchess of Cambridge on the birth of their baby girl. I'm absolutely delighted for them," Prime Minister David Cameron wrote on Twitter.

Deputy Prime Minister Nick Clegg said he and his wife Miriam wished "them all the best as their family grows."

Labor leader Ed Miliband tweeted: "Congratulations to the Duke and Duchess on the birth of their daughter. Wishing them lots of joy and happiness - and hopefully some sleep!"

She gave birth at 8:34 am (0734 GMT), some 2-1/2 hours after having been admitted in the early stages of labour to the the private Lindo wing of St Mary's Hospital, West London, the palace said.

Both families of the couple had been informed, it said, including the new baby's great-grandmother Queen Elizabeth, her grandfather Prince Charles and William's brother Prince Harry.

No name for the newborn has yet been announced.

Prince William, 32, and Kate, 33, 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, the couple will initially return to Kensington Palace for a couple of days before heading to Anmer Hall, their country mansion on the queen's Sandringham estate in Norfolk, eastern England.

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 6 am (0500 GMT).

William was born at the same hospital to the late Princess Diana in 1982.

"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.