"Her Royal Highness The Duchess of Cambridge has been admitted this morning to St. Mary's Hospital, Paddington, London in the early stages of labour," reads an official statement from Kensington Palace. "The Duchess traveled by car from Kensington Palace to the Lindo Wing at St. Mary's Hospital with The Duke of Cambridge."
With Prince William by her side, Kate was already in labor when she was admitted to the hospital just before 6 a.m. in London. The palace has also said her labor is progressing normally.
Shortly after they arrived, a loud clap of thunder was heard over west London.
Since her last official appearance on the balcony of Buckingham Palace during a June 15 ceremony, Kate, 31, has been "winding down," as a royal source put it. William, also 31, has been on leave from his job as a Royal Air Force helicopter search and rescue pilot.
She's been seen browsing antique stores, quietly nesting at home, visiting her parents in Bucklebury, about 55 miles west of London, and conserving her energy. "She's been looking after herself – she just needs to make sure she's okay," a friend tells PEOPLE.
On Saturday, PEOPLE confirmed she and William were at home in Kensington Palace, waiting out the final hours of her pregnancy.
The statement announcing her hospital arrival was the first that Palace officials said they would provide. Once the baby is born, a notice will be posted on a wooden easel just inside Buckingham Palace railings, followed moments later by an electronic message to the media and the world.
Kate is being attended by a team headed by the calm and experienced hands of royal gynecologist Marcus Setchell, 69, and Alan Farthing. There are also thought to be some anesthetists, midwives and nurses attending to Kate.
As for William and Kate, "They are terrifically excited," the friend tells PEOPLE.
Neil P. Mockford / FilmMagic