"A huge clap of thunder sounded over west London shortly after their arrival," reported People magazine.
Kensington Palace waited until the Duchess had been seen by medical staff and was comfortable before making the announcement.
A spokesman for the couple said: "Things are progressing as normal," the Guardian reported. It was believed the labour had not been induced.
The Duchess had been due to give birth in mid-July, meaning she has gone into labour just over a week later than expected.
The world's media has been staking out the hospital since the beginning of July, and more than 200 journalists, photographers and TV cameramen are expected to remain there until the Duchess leaves hospital with her baby.
Last week, the Duke and Duchess were with Kate's parents, Michael and Carole Middleton, in Bucklebury, Berkshire. This led to speculation that the royal birth might actually occur at the Royal Berkshire hospital. But the plan was always for the birth to take place at the Lindo Wing; there were plans to use the Royal Berkshire only in an emergency.
When Diana, Princess of Wales gave birth to Prince William at the same hospital in 1982, she discharged herself just 36 hours after admission. She was in labour for 16 hours, having been admitted between 4pm-5pm.
Prince William was born at 9.03pm (England time) on June 21, with the Prince of Wales by his wife's bedside.
Last month royal aides said that the Duchess had opted to give birth naturally, rather than by an elective caesarean section.
The Duke and Duchess do not know the sex of their baby.
Marcus Setchell, the Queen's former gynaecologist, will deliver the baby, aided by the Queen's current gynaecologist Alan Farthing, the former fiance of the murdered BBC presenter Jill Dando. Mr Setchell has abstained from alcohol since mid-June to make sure he was ready to deliver the baby whenever the call came.
The Lindo Wing charges a basic price of £4965 ($9600) for a "normal" delivery and a 24-hour stay, with each extra night costing an additional £1050 for a deluxe room. The cost of the first 24 hours rises to £6420 if a caesarean section is required.
The prices do not include the fee charged by consultants, and over the course of the entire pregnancy, the bill is likely to be around £12,000.
The first indication that the Duchess has given birth will come when an aide leaves the hospital carrying a piece of paper with details of the baby's sex, weight and time of birth, which they will hand to a driver to be taken to Buckingham Palace.
The Queen, senior members of the royal family, and the duchess's family - if they are not at the hospital - will be told about the birth first.
Then, a royal aide will take the bulletin, signed by key medical staff, from the hospital to the palace under police escort.
The notice will then be placed on an easel on the forecourt of the palace for the waiting world to be given its first information about the future king or queen.
Shortly afterwards, the news will be put out on the palace's official Twitter feed, though aides stressed that no electronic communication would be made until the public had had a chance to see the official notice, as "it's important that this is done with a degree of dignity and with half an eye on the historical significance" of the occasion.
Another change to tradition was the presence of officials in the delivery room. The BBC reported that 42 "eminent public figures" were called in to verify the birth of King James II's son James Francis Edward in 1688.
Bookies have taken a stream of bets on the baby being a boy, partly because the Duchess is reported to have bought a blue pram, but a royal source said: "The Duke and Duchess don't know the sex of the baby and they have decided not to find out beforehand".
If the Duchess gives birth in the middle of the night no announcement is likely to be made until the Queen has woken, as sources said they did not expect her to be woken up specially to be told the news.
The royal couple have so far given no indication as to whether they have chosen names for the baby.
When the Duke of Cambridge was born his name was not announced for a week, reportedly because the Prince of Wales and Diana, Princess of Wales, could not agree on one.
If the royal baby arrives before 11am today (NZT), its birthday will fall under the zodiac sign of Cancer, but if born after then, it will be a Leo.
- Agencies
