"We wish them both the very best and hope Catherine's stay in hospital is a short one. On behalf of the people of New Zealand, I congratulate them both."
Governor-General Sir Jerry Mateparae added his congratulations.
"News of the pregnancy is a wonderful gift to the child's parents, and both of their families, and especially Her Majesty The Queen, who celebrates her Diamond Jubilee this year.
"On behalf of my wife Janine and all New Zealanders, I send our best wishes to the Prince and Duchess at this happy time. I will be writing to Their Royal Highnesses to offer my personal congratulations."
The couple's first child will be third in line to take the throne - leapfrogging the gregarious Prince Harry and possibly setting up the first scenario in which a UK female heir could benefit from new gender rules about succession.
The palace would not say how far along the 30-year-old duchess is, only that she has not yet reached the 12-week mark.
Palace officials said the duchess was hospitalised with hyperemesis gravidarum, a potentially dangerous type of morning sickness where vomiting is so severe no food or liquid can be kept down.
They said she was expected to remain hospitalized for several days and would require a period of rest afterward.
"The best advice for anyone suffering from (severe morning sickness) is to get plenty of rest and drink lots of fluid," Dr Daghni Rajasingam, a spokeswoman for Britain's Royal College of Obstetricians and Gynaecologists, said in a statement.
"The condition usually subsides by week 12 of the pregnancy and with early diagnosis and treatment, there is no reason why we shouldn't expect a healthy pregnancy."
The condition is thought to affect about one in 200 pregnant women, according to Britain's health department.
The news came just days after the duchess, on a royal appearance, played field hockey with children at her former school.
Not only are the attractive young couple popular - with William's easy common touch reminding many of his mother, the late Diana - but their child is expected to play an important role in British national life for decades to come.
William is second in line to the throne after his father, Prince Charles, so the couple's first child would normally become a monarch - eventually.
The confirmation of Kate's pregnancy caps a jam-packed year of highs and lows for the young royals, who were married in a lavish ceremony at Westminster Abbey last year.
They have travelled the world extensively as part of Queen Elizabeth II's Diamond Jubilee celebrations and weathered the embarrassment of a nude photos scandal, after a tabloid published topless images of the duchess.
Joe Little, managing editor of Majesty magazine, said the news bookended a year that saw the royal family riding high in popular esteem after celebrations of Queen Elizabeth II's 60 years on the throne.
"We're riding on a royal high at the moment at the end of the Diamond Jubilee year," he said. "People enjoyed the royal romance last year and now there's this. It's just a good news story amid all the doom and gloom."
Speculation about when the couple would start a family has been rife since their wedding.
Diana got pregnant just four months after her wedding to Prince Charles in 1981. She also reportedly suffered from morning sickness for months and complained of constant media attention.
"The whole world is watching my stomach," Diana once said.
She gave birth to William in 1982 after 16 hours of labor. At his birth, William was given a baby tag marked 'Baby Wales' and a 41-gun salute was fired in Hyde Park and the Tower of London.
In September 1983, roughly a year after the birth of William, Buckingham Palace announced that Diana was pregnant for a second time. However, within a week, Diana suffered a miscarriage when on holiday at Balmoral, Scotland.
In 1984, she became pregnant again and gave birth to Harry.
American tabloid speculation of Kate's pregnancy has been rampant for months. One newspaper even cited anonymous sources talking about Kate's hormone levels. Others have focused on the first signs of the royal bump.
The palace said the royal family was "delighted" by the news. British Prime Minister David Cameron admitted he got a heads-up about the pregnancy, saying he found the news "quite difficult" to keep to himself and expressing his confidence the duo will make "absolutely brilliant parents."
The leaders of Britain and the 15 former colonies that have the monarch as their head of state agreed in 2011 to new rules which give females equal status with males in the order of succession.
Although none of the nations had legislated the change as of September, the British Cabinet Office confirmed that this is now the de-facto rule.
Those changes make Kate's pregnancy all the more significant for the royal family, according to Ingrid Seward, editor-in-chief of Majesty magazine.
"This is the first child who will be an heir to the throne whatever sex they are," she said. "It's a new beginning."
Graham Smith of anti-monarchy group Republic called Kate's pregnancy a "private, personal matter" for her and William, saying the flood of media coverage was disproportionate.
"We've heard today that our future head of state is on the way. It's a pretty bizarre way of choosing someone for public office," he said.
On the couple's tour of Malaysia, Singapore, the Solomon Islands and Tuvalu in September, William reportedly said he hoped he and Kate would have two children.
In the chilly night air at London's Camden market, concert goers and shoppers seemed surprised by the news - though all agreed that it had been widely anticipated.
"It feels a lot like a Christmas present for the nation!" said Ravian Van Den Hil, 26, a student from Rotterdam in the Netherlands. "It makes me feel quite happy."
Others wondered why Britain continues to spend so much supporting the royal family. "I don't think it's a good thing," said Stephen Jowitt, 63, as he strolled down Camden High Street. "It reinforces a class system."
Read more:
Kate Middleton's morning sickness explained
Place your bets: Royal baby name
- AP
