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"Their Royal Highnesses The Duke and Duchess of Cambridge are very pleased to announce that The Duchess of Cambridge is expecting a baby," the prince's office said in a statement, adding that Queen Elizabeth and the royal family were delighted.
The couple, officially known as the Duke and Duchess of Cambridge, married in April last year, amid a global media frenzy and there has been much speculation, particularly in U.S. gossip magazines, about a possible pregnancy.
"It's only been a matter of time. Everyone has been waiting for Kate to announce that she was pregnant," Claudia Joseph, who has written a biography of the duchess, told Reuters.
A spokeswoman for the couple said 30-year-old Catherine, widely known as Kate, was in the King Edward VII Hospital in central London suffering from Hyperemesis Gravidarum, an acute morning sickness which causes severe nausea and vomiting and requires supplementary hydration and nutrients.
Britain's National Health Service website said the condition was common in the early weeks of pregnancy but did not put the baby at any increased risk.
Professor Tim Draycott, a consultant obstetrician at the University of Bristol, told Reuters that the condition may indicate more than one royal baby may be in the offing.
"Hyperemesis is slightly more common with twins " Draycott said.
William, a Royal Air Force helicopter pilot, was at her side and she is likely to remain in hospital for several days. There was no detail about when the baby was due, although the prince's spokesman said she was less than 12 weeks pregnant.
"I'm delighted by the news that the Duke and Duchess of Cambridge are expecting a baby," Prime Minister David Cameron said on his Twitter website. "They will make wonderful parents."
William, Queen Elizabeth's 30-year-old grandson, is second in line to the British throne, and their first child will become the third in succession when he or she is born.
Last year Britain and other Commonwealth countries which have the queen as their monarch agreed to change the rules of royal succession so that males would no longer have precedence as heir, regardless of age.
The agreement also means an end to a ban on a future monarch marrying a Catholic, a stipulation dating back some 300 years.
Britain's royal family are currently riding the crest of popularity on the back of William and Kate's wedding and the queen's diamond jubilee this year which has witnessed nationwide celebrations.
The young royal couple have become global stars after some two billion people tuned in to watch their glittering marriage ceremony and the sumptuous display of pageantry that accompanied it, and barely a day goes by without a picture of Catherine appearing in the pages of Britain's royalty-obsessed newspapers.
The duchess, the first "commoner" to marry a prince in close proximity to the throne in more than 350 years, is now a fashion icon, with her attire scrutinised every time she steps out in public and followed by legions of women around the world.
That has also brought unwanted attention and there was anger in Britain when topless photos of Kate relaxing on holiday were published in a French magazine in September.
The pictures rekindled memories of the media pursuit of William's mother, Princess Diana, who was killed in a car crash in Paris in 1997 while being chased by paparazzi.
"I will be very surprised if this isn't handled with the utmost tact and sensitivity," said media commentator Steve Hewlett. "Newspapers realise there's a huge amount of goodwill towards Will and Kate, and they take their cue from their readers."
Kate made her last public appearance on Friday when she returned to her old school - a minor event that nonetheless generated live television coverage on news channels - when she looked healthy and joined in a game of hockey with pupils.
Earlier in the week William had hinted at a pregnancy during a visit to Cambridge in central England when they were given a home-made baby suit emblazoned with the words "Daddy's little co-pilot", a reference to William's job.
"When I gave it to him he said 'I'll keep that', and handed it to his aide," said Samantha Hill.
Joseph, author of "Kate: The Making of a Princess", said she believed the couple, who currently live in north Wales where the prince is based as a search and rescue pilot, had been waiting for the right moment to have a baby.
"My feeling has always been that they were not going to take the spotlight away from the queen in her Jubilee. But now 2013 is going to be William and Kate's year," she said, adding the couple would make wonderful parents.
"We have seen her with children and she is lovely with them, she's got the natural touch, and her parents run a party business and she has spent a lot of time with children," Joseph said. "(William) he has always talked about wanting children, so I am sure he is delighted."