The Duke and Duchess of Cambridge are expecting their first child, St James's Palace has announced.
The Duchess was admitted to King Edward VII Hospital in central London with severe morning sickness.
As the pregnancy is in its very early stages, she is expected to remain there for the next few days.
Hyperemesis gravidarum is a rare condition which causes severe vomiting during pregnancy and can cause dehydration, weight loss and a build-up of toxins in the blood or urine called ketosis.
The couple made their own way to the hospital from Bucklebury, where she had spent the weekend with her parents, Michael and Carole Middleton.
It is understood the rest of the royal family only learned about the news on Monday.
William was by her side until 8.20pm when he left the hospital without saying a word to the media pack assembled outside.
Members of both families including the Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall, Prince Harry - and the Middletons - are said to be "delighted" with the news.
The baby will be the Middletons' first grandchild and the first for the Prince of Wales, although he plays an active role in the lives of the Duchess of Cornwall's own grandchildren.
William's uncle Earl Spencer said in a statement: "It is wonderful news and I am thrilled for them both."
The baby would have been a first grandchild for William's late mother and the Earl's sister, Diana, Princess of Wales.
The news comes 17 months after William and Kate married at Westminster Abbey on April 29, 2011.
Before their wedding, they both spoke earnestly about the next stage in their life.
Kate, who is close to her own parents and siblings, revealed: "I hope we will be able to have a happy family ourselves."
Her biographer, Claudia Joseph, told Sky News: "I think she will be a lovely mother. She comes from a very stable background herself ... that Kate will replicate."
During the couple's nine-day tour of the Far East and South Pacific in September, the Duke revealed he wanted to have two children with his wife.
The child will be third in line to the throne whether it is a boy or girl.
Prime Minister David Cameron was among the first to congratulate the royal couple on Twitter.
"I'm delighted by the news that the Duke and Duchess of Cambridge are expecting a baby. They will make wonderful parents," he said.
Deputy Prime Minister and Lib Dem leader Nick Clegg tweeted: "Congratulations to the Duke and Duchess of Cambridge on their news - a perfect way to round off the Queen's Diamond Jubilee year."
Labour leader Ed Miliband tweeted: "Fantastic news for Kate, William and the country. A royal baby is something the whole nation will celebrate."
Just a week ago, during the couple's inaugural trip to their dukedom - Cambridge - the Duke, an RAF search-and-rescue pilot, received a home-made romper suit from new mum , Samantha Hill, 27, from Sudbury, Suffolk.
The Babygro was emblazoned with a picture of a helicopter and the words "Daddy's little co-pilot".
The Duke, all smiles, who has made no secret of his desire to start a family, received the gift saying: "Fantastic, I'll keep this."
St James's Palace would not say when the royal couple became aware of the pregnancy - only that it was "recently".
It is understood that the pregnancy has not passed the 12-week point.
A spokeswoman at Kate's old prep school, St Andrew's in Pangbourne, Berkshire - where she showed off her hockey skills last week in an Alexander McQueen frockcoat and three-inch-high calf-length boots - said they had "no inkling at all" that she was expecting.
She said: "Obviously everyone at St Andrew's are delighted for them both. We're absolutely thrilled."
A spokesman for the Royal Air Force, with which William serves as a search-and-rescue pilot, said: "The RAF is delighted with the news and wishes the Duke and Duchess of Cambridge all the best for the future."
The Duchess had a number of engagements this week, including a visit to London's Docklands on Wednesday for a charity fundraising session on a brokers' trading floor, but they have all been cancelled, said St James's Palace.
A spokeswoman for the University of St Andrews, where Kate and William met, said: "We are delighted for the couple and will be writing to them to offer our congratulations. They must be very pleased."
The Archbishop of Canterbury, who married the royal couple in Westminster Abbey in April 2011, said: "The whole nation will want to join in celebrating this wonderful news.
"We wish the Duchess the best of health and happiness in the months ahead."
News that the Duke and Duchess of Cambridge are expecting a baby marks the perfect way to round off the Queen's Diamond Jubilee year.
The news echoes back to the Silver Jubilee of 1977 when the Queen learned that her first grandchild was on its way.
The Princess Royal's pregnancy was described at the time by the Palace as the best Jubilee present of all and Peter Phillips was born in the November of 1977.