St James's Palace says the royal couple had only become aware of the pregnancy "recently".
It is believed that the pregnancy has not passed the 12 week point and the announcement was prompted by the Duchess's medical condition, according to the Press Association.
Keep up to date with the announcement on the ITV News site.
– St James's Palace spokesperson
Their Royal Highnesses The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting a baby.
The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall and Prince Harry and members of both families are delighted with the news.
The Duchess was admitted this afternoon to King Edward VII Hospital in central London with hyperemesis gravidarum.
As the pregnancy is in its very early stages, Her Royal Highness is expected to stay in hospital for several days and will require a period of rest thereafter.
The Duchess of Cambridge is expecting a baby, St James's Palace has confirmed.
The Duke and Duchess live on Anglesey, where Prince William works as an RAF search and rescue helicopter pilot at RAF Valley.