But the palace said the duchess was admitted this afternoon to the King Edward VII private hospital in central London with a severe form of morning sickness known as hyperemesis gravidarum, and is expected to stay in hospital for several days.
St James's Palace said in the statement: "The Duchess was admitted this afternoon to King Edward VII Hospital in central London with hyperemesis gravidarum.
"As the pregnancy is in its very early stages, Her Royal Highness is expected to stay in hospital for several days and will require a period of rest thereafter."
The Queen and Duke of Edinburgh, the Prince of Wales and members of both families are delighted with the news, said a spokesman.
St James's Palace would not say when the royal couple became aware of the pregnancy only saying "recently".
It is understood that the pregnancy has not passed the 12 week point and today's announcement was prompted by the Duchess's medical condition.
For women with hyperemesis gravidarum their vomiting can be so severe they cannot keep food or liquid down.
The condition usually continues past the first three months of pregnancy and can pass by week 21, but may also last longer.
Reacting on Twitter, Prime Minister David Cameron wrote: "I'm delighted by the news that the Duke and Duchess of Cambridge are expecting a baby. They will make wonderful parents."
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."
Kate's visit to her old prep school on Friday afternoon was her last public engagement.
She appeared well and even had lunch at the school with pupils and staff during the two-hour visit.
So her condition may have developed over the weekend and it is likely she was taken to hospital this afternoon after seeking medical advice.
Hyperemesis gravidarum can be serious but Kate was driven to the King Edward VII Hospital in a car and not an ambulance.
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.
Labour leader Ed Miliband responded on Twitter: "Fantastic news for Kate, William and the country. A royal baby is something the whole nation will celebrate."
A spokesman for the Royal Air Force (RAF), 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."
Scottish First Minister Alex Salmond offered his congratulations to the couple, who are known as the Earl and Countess of Strathearn when in Scotland.
Mr Salmond said: "My warmest congratulations and sincere best wishes to the Earl and Countess of Strathearn on this wonderful news. Everyone in Scotland will join me in wishing the couple the very best as they prepare for the birth of their first child."
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."
St James's Palace confirmed that William is by his wife's side in hospital but would not comment on whether he travelled with her to hospital.
Kate made the journey from Bucklebury in Berkshire, where her parents Michael and Carole Middleton live, and it is thought she spent the weekend with them.
William's uncle Earl Spencer welcomed the announcement, saying 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 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."
It is no secret that the Duke and Duchess of Cambridge dreamed of starting a family of their own.
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."
William too expressed his desire to have children with his new wife.
There was speculation that the Duchess, who showed herself to be at ease with youngsters on official engagements, was broody.
Even the food they had shipped to their honeymoon island in the Seychelles - apparently Brussels sprouts - led to suggestion Kate was on a fertility diet aimed at boosting her intake of folic acid.
There will be much excitement among the couple's families.
The baby will be Carole and Michael Middleton's first grandchild and the first for the Prince of Wales - although he is already a doting grandpa to the Duchess of Cornwall's grandchildren.
Yet as well as the personal joy it will bring, William and Kate's child will have a wider historical and constitutional impact: the new baby symbolises the continuation of the monarchy.
He or she is destined to be king or queen and will be born third in line and in direct succession to the throne.
The child will one day be head of the armed forces, supreme governor of the Church of England and head of the Commonwealth, which covers 54 nations across the world, and subsequently head of state of 16 countries.
In blunt terms, Kate will be fulfilling one of her essential duties as a royal wife by producing an heir.
The birth will also expose the Cambridges to a new level of public fascination.
With the world ready to watch their baby grow up, William and Kate will have to balance protecting their prince of princess with the nation's avid interest in its future king or queen.
When William was born, thousands of people gathered outside Buckingham Palace to wait for the birth to be formally announced.
He was the first future British king to be born in a hospital, delivered at the private Lindo Wing of St Mary's Hospital in Paddington, London.
The newborn Prince arrived in June 1982 just under a year after his parents' marriage, while the Queen had Charles in a similar timescale.
When the Queen was born in her grandparents' London home in Mayfair, the home secretary Sir William Joynson-Hicks waited in the next room as part of an age-old custom designed to prevent a substitute baby being smuggled in.
Kate will luckily not have to suffer such ignominy.
The birth of the Queen's cousin Princess Alexandra in 1936 was the last occasion on which the home secretary was present.
King George VI declared that a minister was needed only for those in the direct line of succession, but by the time Charles was born in 1948, the practice had been abandoned after being deemed "neither a statutory requirement nor a constitutional necessity".
Kate will be tended by a top medical team. Royal mothers are usually looked after by the Queen's gynaecologist - currently Alan Farthing, the former fiance of murdered TV presenter Jill Dando.
The birth of the prince or princess follows a radical shake-up of the monarchy's successions rights.
Prime Minister David Cameron announced in October last year that the 15 other Commonwealth countries where the Queen is head of state had agreed to give female royals the same rights of succession as their brothers.
"Put simply, if the Duke and Duchess of Cambridge were to have a little girl, that girl would one day be our queen," Mr Cameron said.
When the law goes through, first-born royal daughters in direct line to the throne will no longer be leapfrogged by their younger male siblings.
The proposed constitutional change was spurred by the marriage of the Duke and Duchess of Cambridge in anticipation that they would produce a child.
The Duke and Duchess of Cambridge's baby will be born third in line to the throne and a great grandchild to the Queen.
The last time a still-serving monarch got to meet a great grandchild born in direct succession to the crown was nearly 120 years ago.
Queen Victoria, who reigned until 1901, was still sovereign when her great grandchild Edward VIII, who later abdicated, was born third in line in 1894.
His brother George VI was also born in Queen Victoria's lifetime, arriving fourth in line in 1895.
The last great granddaughter of a still-serving sovereign born in direct succession on the male line was their sister Princess Mary in 1897.
William and Kate's baby - a future King or Queen - will be the great great great great great grandchild of Queen Victoria.
When the newest addition to the Royal Family arrives, Prince Harry, the baby's uncle, will be bumped down the line of succession to fourth place.
The Queen has already welcomed her first great grandchild, Savannah Phillips - the daughter of Peter and Autumn Phillips - but Miss Phillips is only 12th in line, being born down the female line as a granddaughter to the Princess Royal. Her second great grandchild - Savannah's sister - Isla was born in March 2012, 13th in line to the throne.
Royal births are usually celebrated with a Royal Salute of 41 guns.
They are registered in the normal way, although the Home Secretary is required to notify certain officials including the Lord Mayor of London, while the Queen's Private Secretary Sir Christopher Geidt informs Governor Generals overseas.
There is also the age old custom of attaching Notice of Royal births and deaths to the railings at Buckingham Palace for members of the public to read.
But as well as keeping to this tradition, the arrival of royal birth will no doubt also be officially declared via the monarchy's websites, on Facebook and via Twitter.
Bookmakers will be taking flurries of bets on what the Duke and Duchess of Cambridge will choose to call the eagerly anticipated new Prince or Princess.
Speculation as to what they might name their first child began even before Kate was pregnant with predictions posted ranging from Mary and Matilda to Edmund and George on the mumsnet website before their wedding.
Their decision - be it traditional or unusual - will most likely set a trend for the next generation of babies.
Royal youngsters are mostly given safe, historical names which are passed down through the monarchy such as James, Edward, Charles, George, Mary and Elizabeth.
William and Kate will also be mindful of choosing a name that befits a future King or Queen. This royal baby will be born third in line to the throne.
If Kate gives birth to a girl, many will expect the Duke and Duchess to pay homage in some way to William's late mother Diana, Princess of Wales, as well as to the Queen. Likewise, the arrival of a boy could see a tribute to the Duke of Edinburgh, the Prince of Wales or even Prince Harry. But the Cambridges are also likely to take inspiration from Kate's side of the family.
Royal children often boast an array of middle names - William's own being Arthur Philip Louis - so the couple are likely to pick several - offering them the chance to include a nod to both sets of relatives.
They also might incorporate a Welsh name to reflect their links to Wales, a name with historical connections to the city of Cambridge or perhaps something Scottish to represent the time they spent together in St Andrews.
Linda Rosenkrantz and Pamela Redmond Satran, the authors of Cool Names for Babies, already have their predictions on the babyzone website - posted before Kate was even pregnant.
Suggestions include Alice (the name of Queen Victoria's second daughter and also the Duke of Edinburgh's mother), Amelia (George II's second daughter), Dorothea (meaning gift of god) and Charlotte (wife of George III) for a girl and Augustus (George II's middle name), Frederick (a son of George III) or Leopold (a son of Queen Victoria).
If the baby is boy, he would be expected to be styled a Prince and if the baby was a girl, a Princess.
The last example of a great granddaughter of a still serving Sovereign born on the male line was Princess Mary, who was born in 1897 and was George VI's sister and a great granddaughter of Queen Victoria.
As to the child's surname, according to the monarchy's official website: "For the most part, members of the Royal Family who are entitled to the style and dignity of HRH Prince or Princess do not need a surname, but if at any time any of them do need a surname (such as upon marriage), that surname is Mountbatten-Windsor."
In 1917, George V adopted Windsor as the royal family's House and surname. In 1960, for the direct descendants of the Queen and the Duke of Edinburgh who require a surname, it became Mountbatten-Windsor. Mountbatten was the surname Greek-born Prince Philip assumed when he became naturalised in 1947.
William has used Wales professionally in the forces. His children might use Cambridge in the same way, or even Wales too as William still retains his title Prince William of Wales.
If a boy, the baby is also likely to one day be Prince of Wales. The title is usually given to the male heir to the throne, but it is not automatic.