It is a historic moment for the British monarchy — the couple's first child will become third in line for the British throne, after Prince Charles and William, and should eventually become king or queen.
William and Kate entered St. Mary's Hospital in central London through a side door early Monday morning, avoiding the world's media. Palace officials confirmed her arrival about 90 minutes later.
Royal officials said they traveled by car, without a police escort, just before 6 a.m. Kate — also known as the Duchess of Cambridge — is expected to give birth in the private Lindo Wing of the hospital, where Princess Diana also gave birth to William and his younger brother, Prince Harry.
"Things are progressing as normal," the couple's spokesman said.
She will be looked after by a top-notch medical team led by royal gynecologist Dr. Marcus Setchell. Palace officials are not expected to provide many details about how her labor is progressing.
The baby is in line to become Britain's monarch and be recognized as head of state in 15 other countries, including Canada and Australia, playing a leading role in charting the future of the Commonwealth.
But little else is known, including how the baby will arrive — it is not clear if Kate will have a natural birth or deliver by a planned cesarean section — its gender and its name.
Royal watchers must wait to be told of the baby's arrival from the palace, which is planning to reveal the news through a mixture of tradition and social media.
Palace officials have said that the first hint will come when a royal aide emerges from the hospital with a signed bulletin carrying the Buckingham Palace letterhead. The bulletin will be given to an official who will be driven to Buckingham Palace, where it will be posted on an easel in public view in front of the building.
At the same time the bulletin is posted, there will be an official announcement on Twitter and the media will be formally notified. The document will give the baby's gender, weight and time of birth.
It could be some time before the baby's name is made public. When William was born, a week passed before his name was announced. Charles's name remained a mystery for an entire month.
But it is the baby's gender that is of particular interest because the prospect of Kate's pregnancy prompted a change to laws of succession to ensure a daughter would not be passed over for the crown by a younger brother. Boy or girl, the child will be the prospective future monarch.
The birth of a new heir to the throne has been breathlessly anticipated by many Britons since William and Kate wed on April 29, 2011.
Reflecting the fact that not everyone is so excited, however, the Guardian newspaper added a "republican" button to its website so that those who are not in favor of the monarchy could get a baby-free version of the paper.
Despite a rough start to the pregnancy, when she was hospitalized for acute morning sickness, the 31-year-old Kate made a number of public appearances that were halted only near the end of her term.
Since the duchess has cut back on her royal duties, media outlets have been clamoring for position outside of the hospital in anticipation of the birth, jockeying to secure the best vantage point for filming William and Kate emerging, babe in arms.
At Buckingham Palace, where the birth will be announced, tourists packed near the front gate, peering through the black iron bars to catch of a glimpse of any action.
Two New York teachers, Maddalena Buffalino, 29, and Michael Savino, 32, were quizzing a pair of passing police officers about where the easel would be placed.
"Just being here is very cool," said Buffalino, who said she'd been following royal baby news intently.
She said the tradition and glamor of the royal household was what attracted Americans like her to the palace.
"It's the history," the social studies teacher said. "We don't have it."
Police eventually shooed the growing crush of tourists away from the gate, with one officer warning the assembled crowd to keep an eye on their wallets and valuables.
Officials have said that William plans to take two weeks' paternity leave and then return to his military duties as a search-and-rescue helicopter pilot in Wales.
His tour of duty is scheduled to wrap up around September, and he and Kate are expected to move from their isolated cottage on the island of Anglesey off the coast of Wales to Kensington Palace in central London.
But major refurbishment works at the palace likely won't be finished until at least a month or two after the infant is born — meaning that William and Kate will most likely have to make do with their current temporary home in London, a two-bedroom property at the palace.
Come autumn, however, the family will be able to move into their permanent London home, Apartment 1a at Kensington Palace — a four-story house with a nursery, 20 rooms and a private garden.