Prince William and his wife Catherine's first child is due in July, St James' Palace announced on Monday, adding that the mother-to-be is feeling better following her hospitalisation last month.
"Their Royal Highnesses The Duke and Duchess of Cambridge are delighted to confirm they are expecting a baby in July," the palace said in a statement, suggesting the 31-year-old is at least three months pregnant.
"The duchess's condition continues to improve since her stay in hospital last month," it added.
Catherine was admitted to hospital on 3 December suffering from hyperemesis gravidarum, a severe form of morning sickness, and stayed three nights.
She was not seen in public for several weeks after receiving treatment, although she presented cyclist Bradley Wiggins with the BBC's Sports Personality of the Year award shortly before Christmas.
Last week she was photographed attending a performance of the Cirque du Soleil in London for her birthday, and also attended the unveiling of her first official portrait at the National Portrait Gallery, where she looked well.
Her hospitalisation had forced royal officials to announce her pregnancy before she had yet reached 12 weeks, the point at which the danger of a miscarriage drops off significantly.
Hyperemesis gravidarum is often associated with twins, but the palace confirmed on Monday that William and Kate were only expecting one child. They refused to comment on its sex, or whether the couple knew its sex.
The child will be direct in line to the throne after William and his father Prince Charles, and should wear the crown regardless of whether it is a boy or a girl thanks to a change in the laws of succession.