The Duke and Duchess of Cambridge's baby is due in July, St James's Palace has announced.
Kate's condition is also continuing to improve following her stay in hospital last month for severe morning sickness, said a spokesman for the couple.
The Duchess is believed to be around 13 to 14 weeks pregnant and confirmation of the birth month means it is likely she has now had her 12-week scan.
"Their Royal Highnesses the Duke and Duchess of Cambridge are delighted to confirm they are expecting a baby in July," said a St James's Palace spokesman. "The Duchess's condition continues to improve since her stay in hospital last month."
The update is also further confirmation that Kate is expecting just one baby. There had been speculation that she might be carrying twins.
The Duchess is suffering from hyperemesis gravidarum, which causes severe vomiting during pregnancy and is more often experienced by women expecting twins. The condition is most common in the first 12 weeks of pregnancy and often eases off in the second trimester of pregnancy, which Kate is believed to be entering now.
At the start of the second trimester, the baby's fingers and toes have separated and its nails are beginning to form. Some babies even start sucking their thumbs.
Kate was last seen in public last Friday when she visited the National Portrait Gallery in London with William for the unveiling of her first official portrait. She looked well and smiled during the brief appearance, with some commentators spotting the start of a slight baby bump.
If the new prince or princess 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 due date looks likely to be around mid-July.
A spokesman for the couple said they were unlikely to undertake any engagements in the next few weeks as William would be concentrating on his flying with the RAF Search and Rescue Force. He added that Kate was likely to return to engagements "in the near future".
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