According to the palace statement, Queen Elizabeth II and both families are said to be “delighted with the news”.
As with her previous two pregnancies, Kate Middleton, 35, is suffering from hyperemesis gravidarum, or severe morning sickness.
The duchess will no longer carry out her planned engagement at the Hornsey Road Children’s Center in London on September 4.
She is being cared for at Kensington Palace, the statement said.
Prince William and Kate Middleton have one son, George, and one daughter, Charlotte, aged 4 and 2.
With the previous two pregnancies, the royal couple was forced to announce them before the 12-week mark because of the duchess being unwell with hyperemesis gravidarum.
Kate Middleton’s first pregnancy was revealed when she was just a few weeks pregnant with Prince George after she was admitted to hospital in December 2012.
Her second pregnancy with Princess Charlotte was announced in September 2014, when she was treated at the palace for the condition.
Hyperemesis gravidarum affects about one in every 200 pregnancies and results in severe nausea and vomiting – with one of the main dangers being dehydration.
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