The Duchess of Cambridge is pregnant with her second child.
Kensington Palace said the Queen and members of both families were delighted with the news.
The palace said that - as when she was pregnant with Prince George - the duchess was suffering from very acute morning sickness and was being treated by doctors at Kensington Palace.
Prime Minister David Cameron tweeted he was "delighted by the happy news that they're expecting another baby".
The duchess will no longer accompany Prince William on their planned engagement in Oxford on Monday, Clarence House said.
The sickness - called hyperemesis gravidarum - is a condition that may require supplementary hydration, medication and nutrients.
Clarence House said: "Their Royal Highnesses the Duke and Duchess of Cambridge are very pleased to announce that the Duchess of Cambridge is expecting their second child."
Mr Cameron offered his "many congratulations".
Catherine had been due to join William in formally opening a £21m China study centre at Oxford University.
The baby announcement came two months after the couple's first child, Prince George, had his first birthday.
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