Prince William and wife Kate are expecting their third child

Reporting from London —  Prince William and wife Catherine, the Duchess of Cambridge, will soon welcome a third child to the royal nursery.

Kensington Palace officials announced Monday that the duchess is pregnant, but was not feeling well enough to attend an engagement later in the day.

As with her other two pregnancies, the duchess, the former Kate Middleton, is suffering from hyperemesis gravidarum, or acute morning sickness. She is being cared for at the royal couple’s apartment in London’s Kensington Palace.

The sickness failed to put a damper on the buoyant mood among the British royals, however. Prince Harry will be bumped down in the line of succession, but was overjoyed, describing the news as “fantastic,” and offering a thumbs up while on a visit to Manchester.

And asked how the duchess was, he said, “I haven’t seen her for a while but I think she’s OK.”

No details were immediately available about when the third baby is due, though the duchess is less than 12 weeks pregnant. That would put the due date somewhere between mid-March and mid-June.

William and Catherine, both 35, already have two children: Prince George, 4, and Princess Charlotte, 2.

The announcement comes as the royal couple prepared to mark another milestone for their young family: George is scheduled to start school Thursday at Thomas’s Battersea in South London.

Their choice of a south London school indicated that the royal couple were settling into their Kensington Palace apartment, having moved recently from their Norfolk home, Anmer Hall.

Betting agencies were quick to start offering odds on possible names for the soon-to-be addition to the House of Windsor.

Paddy Power offered 8-to-1 odds on Alice and 10-to-1 odds on Arthur. Also popular is Diana, after William’s mother, particularly given the timing of the announcement.

William and the duchess took a leading role in marking the 20th anniversary of Diana’s death last week. The couple, joined by Harry, toured the garden of Kensington Palace to commemorate the princess’ contributions to their family and the many charities she supported.

“Given the recent anniversary, there’ll be plenty of interest in the name Diana if the baby is a girl,” Paddy Power said.

When asked on a royal tour in Singapore in 2012 about how many children he wanted, William said he was “thinking about having two.”

More recently, during a royal tour of Poland, the duchess joked about a third child when she was given a cuddly toy designed to soothe tiny babies.

She thanked the well-wisher for the present and turned to William.

“We will just have to have more babies,” she said, laughing.

The duchess is the eldest of three siblings and reportedly had a very happy childhood. William and Harry are the only children of Prince Charles and Princess Diana.

Visitors to the palace Monday welcomed the news. Elizabeth Hopkins, 79, from West London was delighted and said Britain needs lots of royal children.

“They’re lovely and, you know, going around with a lot of children brings out the best in people as well,” she said. “And they’ve obviously very happy children and in a happy group, so I think it’s all the best for them.”

Others said the world would be watching.

Katherine Redo, 34, who lives in London but is originally from Metairie, La., held tight to her squirming 2-year-old daughter, Annabelle, and said she believed many people in the United States would be happy for the royal couple.

“It’s sweet because usually it’s just an heir and a spare and they’re having a third,” she said. “It just gives the idea or the impression that they’re just even more the sweetest, perfect little family.”

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UPDATES:

4:00 p.m.: This article has been updated with details, background.

This article was originally posted at 2:40 a.m.