The Duke and Duchess of Cambridge, as the couple are officially known, drove from their home Kensington Palace in central London to St Mary's Hospital in west London where their other two children, George and Charlotte, were also born.
"The Duchess of Cambridge was admitted to St. Mary's Hospital, Paddington, London, earlier this morning in the early stages of labour," Kensington Palace said in a statement.
The new royal will be fifth-in-line to the British throne behind siblings Prince George, 4, and his two-year-old sister Princess Charlotte, William, and grandfather and heir Prince Charles.
William's younger brother Harry, who marries US actress Meghan Markle next month, will fall to sixth on the list.
As with her two previous pregnancies, Kate, 36, suffered from hyperemesis gravidarum, an extreme form of morning sickness which can cause severe nausea and vomiting and require supplementary hydration and nutrients.
Kate's last engagement ahead of the birth was on March 22 when she and William attended a number of events in London to celebrate the Commonwealth ahead of a meeting of its leaders last week.
Having had homes in north Wales and Norfolk in eastern England, William and Kate now live at Kensington Palace to allow the prince to dedicate more time to royal duties on behalf of his grandmother.
The British royals are rarely out of the media glare, but the baby arrives at a time when the Windsors have particularly been in the limelight.
On Saturday, Queen Elizabeth celebrated her 92nd birthday attending a televised concert, having played a prominent role at the Commonwealth Heads of Government meeting in London where it was announced Charles would succeed her as head of the network of mainly former British colonies.
The impending birth will also give Kate's family another cause for celebration after it was reported by British media on Sunday that her sister Pippa was pregnant with her first child.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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