The Duchess of Cambridge has been admitted to hospital in the early stages of labour.
Kate was taken to the Lindo Wing at St Mary's Hospital in west London where her first child, Prince George, was born in July 2013.
Kensington Palace said the duchess travelled from the palace with her husband Prince William.
Officials have said the duchess and the prince do not yet know whether the baby is a boy or a girl.
The new baby will be fourth in line to the throne, behind his or her grandfather Prince Charles, father Prince William and brother Prince George.
Prime Minister David Cameron told the BBC Breakfast it was "very exciting news".
He added: "With the rest of the nation I'll be wishing them well today, hoping for a healthy and happy outcome."
Labour leader Ed Miliband said: "I want to pass on my best wishes to the Duchess of Cambridge. My thoughts are with her and the Duke of Cambridge today. I wish them well."
Deputy Prime Minister Nick Clegg tweeted: "Best of luck to the Duchess of Cambridge today, as she gives birth to her second child. The thoughts of the whole country will be with her."