The baby will be third in line in succession to the throne.
The duchess and Prince William married at Westminster Abbey in April 2011. The duchess was last seen in public Friday while visiting her alma mater, St. Andrew's School in Pangbourne in Berkshire.
A spokesperson said the duchess had been admitted to King Edward VII Hospital in central London with acute morning sickness and was expected to stay for several days.
Members of the royal family and the duchess's family, the Middletons, were said to be delighted.
"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," St. James's Palace said in a statement.