The royal baby is here. What happens next, however, is shrouded in uncertainty, and no small amount of pomp and ceremony.
The family were guided through the birth by a top medical team, led by the Queen's former gynaecologist Marcus Setchell. He was made a Commander of the Royal Victorian Order in 2004, in honour of the life-saving care he has provided while presiding over difficult royal births in the past.
Other members of the royal family were not expected to attend the birth, as the heightened security operation required would inevitably disrupt the operation of the hospital.
In the past, royal births could be attended by any number of cabinet ministers, who were traditionally required to confirm that the heir to the throne had not be swapped for another at birth. The practice, while still adhered to even under King George VI for those who were in the direct line of succession, had been abandoned by the time the Prince of Wales was born in 1948.
Ms May will nonetheless have a role to play when the baby is born. While it will receive an official birth certificate in the same way as any other child, the Home Secretary is required to notify certain officials including the Lord Mayor of London, the Governors of Northern Ireland, the Channel Islands and the Isle of Man.
The Queen's most senior aide, private secretary Sir Christopher Geidt, will inform all Governor Generals overseas.
The Queen will, perhaps fittingly, be the first person to be informed of progress, and will receive a phone call from William as soon as anything happens, according to former press secretary to the Queen Dickie Arbiter.
Shortly afterwards, gynaecologist Marcus Setchell will write a formal, most likely typed proclamation, confirming the sex of the baby and possibly its weight. This will be placed in a dark wooden frame, taken away with a police escort and placed in an ornate easel behind the railings at Buckingham Palace.
The birth is expected to then be met with the traditional celebration of a 41-gun Royal Salute.
In a first for such a high profile royal birth, the news will be announced at a similar time across the royal household's "online profile" - its website, Facebook page, and Twitter account @BritishMonarchy.
Any official statements on the birth are expected to be brief, in keeping with the two-paragraph confirmation that the Duchess had gone into labour, and the most the assembled press outside the hospital are hoping for is a very brief appearance from the married couple and baby.
In due course the baby will receive a name, though it is unlikely to be immediate. When William was born the public had to wait a full seven days for an announcement of his name, while the same news for the child's grandfather Prince Charles was only revealed a month after his birth, just before he was christened.
Even if the baby is born promptly today, it is expected that the family will stay overnight at the hospital, and while William will take paternity leave from his job as an RAF search and rescue pilot, it is unclear how long it will be before either returns to official royal duties.
With everyone in the country on the edge of their seats awaiting news of the next step in what has been affectionately dubbed "the Great Kate Wait", employers and royal fans alike will be wishing the Duchess a safe, and swift, delivery.
Video: Prime Minister David Cameron on the royal baby