A statement from the royal household said: "Their Royal Highnesses The Duke and Duchess of Cambridge are delighted to confirm they are expecting a baby in April 2015.
"The Duchess of Cambridge continues to be affected by Hyperemisis Gravidarum, but her condition is steadily improving."
Duchess Kate will give birth to her second child in April 2015
The announcement seems to suggest that the Duchess has passed the 12-week mark. In another sign that her health is improving the young mother will return to public duties this week for the first time since announcing her pregnancy.
Kate is expected to join her husband in greeting the President of Singapore and his wife on behalf of the Queen when they arrive on a state visit on Tuesday. The Cambridges will meet President Tan at the Royal Garden Hotel, London, before travelling accompanying him down Horse Guards Parade to receive a ceremonial welcome.
William and Kate are returning a favour as the president hosted them on their tour of Asia in 2012.
William and Kate announced the pregnancy shortly after Prince George's first birthday
Later in the day, the expectant royal will be at the Natural History Museum.
In her capacity as patron of the museum, Kate will present awards at the Wildlife Photographer of The Year ceremony – an engagement she must really be looking forward to. A keen photographer herself, she has previously released her own images of the rain forest in Borneo, taken on the 2012 Jubilee tour.
The last time she was at the museum was for a charming photo session marking Prince George's first birthday.