The Queen and both families are said to be "delighted with the news."
The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting their third child pic.twitter.com/DZCheAj1RM
As with her previous two pregnancies, the Duchess is suffering from hyperemesis gravidarum, or severe morning sickness.
She will no longer carry out her planned engagement at the Hornsey Road Children's Centre in London today.
Catherine is being cared for at Kensington Palace, the statement said.
The Duke and Duchess have one son, George, and one daughter, Charlotte, aged four and two.
With the previous two pregnancies, the couple were forced to announce them before the 12-week mark because of the duchess being unwell with hyperemesis gravidarum.
Her 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.
The expectant child will become the fifth in line to the throne behind Prince Charles, Prince William, Prince George and Princess Charlotte.
The child will be the Queen's sixth great-grandchild.
Photo: Supplied / Kensignton Palace The Duke and Duchess of Cambridge