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.
The baby will become fourth in line to the throne, moving Prince Harry further down the line of succession.
Prime Minister David Cameron, Labour leader Ed Miliband and the Archbishop of Canterbury were among those to offer their congratulations to the couple.
BBC royal correspondent Peter Hunt said that the Duchess of Cambridge’s morning sickness meant the announcement had had to be made before the 12th week of her pregnancy.
Our correspondent added that said this pregnancy was likely to generate excitement but was lacking the constitutional significance of Prince George’s birth – as things stand the unborn boy or girl is not destined to be monarch.
Her first pregnancy was revealed when the duchess was just a few weeks pregnant after she was admitted to hospital suffering from severe morning sickness in December 2012.
Unlike when she was pregnant with George, the duchess is being treated at Kensington Palace and not at a hospital.
The sickness – called hyperemesis gravidarum – is a condition that may require supplementary hydration, medication and nutrients.
It affects 3.5 per 1,000 pregnancies, causes severe vomiting and can lead to dehydration, weight loss and a build-up of toxins in the blood or urine, called ketosis.
Catherine had been due to join William in formally opening a £21m China study centre at Oxford University but the palace said her morning sickness meant that she would no longer accompany Prince William.
The duchess had been due to carry out her first solo overseas tour in Malta later this month.
The baby announcement came two months after the couple’s first child, Prince George, had his first birthday.
Mr Cameron said: “Prime Minister David Cameron said: “Many congratulations to the Duke and Duchess of Cambridge. I’m delighted by the happy news that they’re expecting another baby.”
Mr Milliband said: “Fantastic to hear that Prince George will soon be a big brother! Congratulations to the Duke and Duchess of Cambridge on their happy news.”