Prince William and his wife Catherine's first child is due in July, St James's Palace announced on Monday.
The palace also said the mother-to-be was returning to full health following her hospitalisation last month with severe morning sickness.
"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 duchess is at least three months pregnant.
"The duchess's condition continues to improve since her stay in hospital last month," it added.
The brief update comes at a time when William and 31-year-old Kate had most likely intended to announce the pregnancy.
But when Catherine was admitted to hospital on December 3 suffering from hyperemesis gravidarum, a condition that makes it hard to keep down food or liquids, the royal couple were forced to reveal the news.
She stayed in hospital for three nights and was not seen in public for weeks after leaving hospital, although she presented the BBC's Sports Personality of the Year award to cyclist Bradley Wiggins shortly before Christmas.
Last week the duchess appeared to be back to full health as she watched a performance of the Cirque du Soleil in London for her birthday.
On Friday, she attended the unveiling of her first official portrait at the National Portrait Gallery, declaring the painting "amazing."
Catherine's 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.
If the baby arrives early, he or she could share a birthday with William's mother, the late Diana, Princess of Wales, who was born on July 1.
The child will be direct in line to the throne after William and his father Prince Charles, and should become monarch regardless of whether it is a boy or a girl thanks to a change in the laws of succession.
New legislation is due to pass through parliament that will end the system of male primogeniture that gave men precedence over women in line to the throne.
William's father Prince Charles has spoken about how the prospect of becoming a grandfather has strengthened his long-held environmental beliefs.
Charles, who will inherit the throne from Queen Elizabeth II, said in a TV interview last week that he did not want to "hand on an increasingly dysfunctional world" to the next generation.
An Indian-born nurse who worked at the private London hospital where Catherine was treated committed suicide in December after she was the victim of a prank call by two Australian radio DJs posing as Queen Elizabeth II and Prince Charles.