The Duke and Duchess of Cambridge's baby is due in July, St James's Palace have announced.
Kate's condition is also continuing to improve following her stay in hospital last month for severe morning sickness, a spokesman for the couple said.
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," a St James's Palace spokesman said.
"The Duchess's condition continues to improve since her stay in hospital last month."
The announcement also appears to lay to rest speculation that the pair are expecting twins, as the statement specified the couple are expecting "a baby".
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".
The Queen has already acted to ensure the new baby - a future King or Queen - will be entitled to be a Princess if William and Kate have a daughter.
Under past rules, a daughter would have been styled Lady instead and not known as Her Royal Highness - only a first-born boy born to the Cambridges would automatically have become a Prince.
Kate is expected to cut down on Royal engagements in the coming months
The Queen 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."
A Letters Patent in 1917, issued by William's great great grandfather King George V, limited titles within the Royal Family.
Kate's pregnancy was announced earlier than planned on December 3 after she was admitted to King Edward VII's Hospital suffering from severe morning sickness.