The Duke and Duchess of Cambridge's summer baby is due in July, St James's Palace has confirmed.
Kate, who was treated in hospital last month for severe morning sickness, is continuing to feel better as she enters the second trimester of her pregnancy.
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 and the pregnancy is progressing well.
Although St James's Palace declined to confirm the exact due date, Kate looks set to give birth to the future King or Queen in mid-July.
"Their Royal Highnesses the Duke and Duchess of Cambridge are delighted to confirm they are expecting a baby in July," a St James's Palace spokesman said. "The Duchess's condition continues to improve since her stay in hospital last month."
The brief update comes at a time when William and Kate had most likely intended to announce the pregnancy. The news was revealed earlier than planned on December 3 after Kate was admitted to King Edward VII's Hospital suffering from hyperemesis gravidarum, which causes severe vomiting during pregnancy.
St James's Palace also confirmed that Kate is expecting just one baby. There had been speculation that she might be carrying twins as hyperemesis gravidarum is more often experienced by women expecting twins.
Kate was last seen in public on 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.
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".
The Queen has already acted to ensure the new baby - a future monarch - will be entitled to be a Princess if William and Kate have a daughter. She has issued a Letters Patent under the Great Seal of the Realm declaring: "all the children of the eldest son of the Prince of Wales should have and enjoy the style, title and attribute of royal highness with the titular dignity of Prince or Princess prefixed to their Christian names or with such other titles of honour."