Kate, 32, and Prince William, 32, are already parents to Prince George, 1. Their second child is expected next year, the palace said.
Buckingham Palace said the Queen and members of both families are delighted with the news.
As with her first pregnancy, Catherine is suffering from hyperemesis gravidarum - or acute morning sickness.
She would not be accompanying Prince William on their planned engagement in Oxford today, the statement said.
"The Duchess of Cambridge is being treated by doctors at Kensington Palace."
Williams and Kate have long spoken of their desire to extend their family, and the timing of the announcement is significant.
William recently announced his decision to put off becoming a full-time working royal in favour of taking a new role as an East Anglian air ambulance pilot.
The new position will allow the couple to bring up their family in the relative privacy of their new home in Norfolk, Anmer Hall.
UK Prime Minister David Cameron also tweeted his well wishes.
"Many congratulations to the Duke and Duchess of Cambridge. I'm delighted by the happy news that they're expecting another baby," he wrote.
The Daily Telegraph reports that it means Prince George will have a brother or sister in the spring of 2015. The new baby will replace Prince Harry as the fourth in line to the throne.
