Duchess of Cambridge gives birth to 8 pound, 7 ounce baby boy, Kensington Palace reports.
The palace says the child was born at 11:01 am local time (10:01 pm NZ Time), a few hours after Kate was admitted to London's St. Mary's Hospital in labour.
Prince William was present for the birth of his son, who is fifth in line to the throne.
The palace says "the queen, The Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news."
Catherine travelled by car from Kensington Palace to the Lindo Wing at St Mary's Hospital with William, The Duke of Cambridge.
Catherine and William have two older children, George, 4, and Charlotte, 2.
A brief formal announcement - on foolscap-sized paper set in a dark wooden frame - will be placed on an ornate golden easel on the forecourt of the palace.
It confirms the sex of the baby and the time of birth, but gives little else away, other than usually revealing that the baby has been "safely delivered" and mother and child are "doing well".
It used to be hand-written, but is now typed.
It will also be signed at the hospital by the doctors who tended to the Duchess, and then ferried back to the palace by car.
Just like with George and Charlotte, an initial official announcement will be emailed to the press by Kensington Palace, coinciding with a confirmation of the birth via Twitter.
News of a new prince or princess is unlikely to be announced overnight as the Queen and members of both families will have to be informed first.
The names given to royal babies are not usually revealed straight away, and the public is often left guessing for several days.
William and Kate took two days to announce both George and Charlotte's names, informing the Queen of their choice beforehand.
The birth will be celebrated with a 41-gun salute in Green Park or Hyde Park - and a 62-gun salute at the Tower of London.
Aunt Meghan and Uncle Harry will be on hand to dote on the royal baby when the prince or princess arrives.
The couple are neighbours of the Duke and Duchess of Cambridge at Kensington Palace, living in Nottingham Cottage in the grounds of the royal residence.
US star Meghan Markle recently hinted at having her own children with Prince Harry.
On a trip to Belfast, the American former actress joked when she was shown an innovative range for newborns: "I'm sure at some point we'll need the whole [lot]."
In an interview in 2016, Markle said becoming a mother was on her "bucket list".
"I can't wait to start a family, but in due time," she said.
Harry has also said he would love to have children.
The topic cropped up in the couple's engagement interview.
"You know, I think one step at a time, and hopefully we'll start a family in the near future," the prince said.
Markle has been spending time getting to know William and Kate's eldest children, Prince George and Princess Charlotte.
The celebrity, who shot to fame playing paralegal Rachel Zane in the American drama Suits, already has two "fairy god-daughters".
She described the children of her close friend Benita Litt as such in a 2016 post on her since-deleted Instagram account.
The bride-to-be and Prince Harry, who will wed in Windsor on May 19, will be among close family expected to attend the christening of William and Kate's baby in a few months.
The dilemma of what to call the latest addition to their family is something the Duke and Duchess of Cambridge will be wrestling with but Mary is the public's favourite moniker.
Punters have been betting that William and Kate will name their baby - which they think will be a girl - Mary, a name which has a long association with the British monarchy.
One British bookmaker has made the name its 3-1 favourite followed by Alice 6-1 and Victoria 8-1, while another prominent UK bookmaker has Mary and Alice as its joint favoured monikers at 5-1, with Victoria next with odds of 8-1.
For boys' names, Albert, Arthur and Fred are all at odds of 14-1 with the first bookmaker, while the other has Albert and Arthur at 12-1, and a number of names at 16-1 including Fred and Philip.
William's great-great-grandmother, the wife of George V, was called Mary, a woman who the Prince of Wales still speaks of fondly, and Mary is one of the Queen's middle names.
Britain has seen two Marys on the throne - Mary I, known as Bloody Mary for her persecution of Protestants, and Mary II, who ruled jointly as monarch with her Dutch husband, William III.
If William and Kate have a girl they may be considering naming her Alice which was the name of the Duke of Edinburgh's mother.
Princess Alice of Battenberg was born deaf but learned to speak and lip-read four languages, and married Princess Andrew of Greece in 1903. Her grandmother was another Princess Alice - the third child and second daughter of Queen Victoria - who lived in Germany after marrying Prince Louis of Hesse.
The new royal baby - William and Kate's third child - will be born fifth in line to the throne. Once the prince or princess arrives, Prince Harry will shift down the line of succession to sixth place.
The Duke of York will move to seventh and Princesses Beatrice and Eugenie to eighth and ninth.
Prince George and Princess Charlotte's younger sibling will be the Queen's sixth great-grandchild, and also a great-great-great-great-great-grandchild of Queen Victoria.
It was always thought that the duke and duchess would go on to have three children. Kate is one of three and is close to both of her siblings.
She joked in the months leading up to her due date that her husband was "in denial" about having a third.
By having more than two children, William and Kate are following in the footsteps of the Queen and Prince Philip, who went on to have four children - although there was a gap of 10 years between their second child, Anne, and third, Andrew.
As a sibling to both future king George and "spare to the heir" Charlotte, the new baby is unlikely ever to be crowned sovereign.
Prince Andrew is the Queen and Philip's third child, but when he was born in 1960 he leapfrogged his older sister, Princess Anne, in the line of succession.
If the Cambridges' third child is a boy, he will no longer be allowed to jump ahead of older sister Charlotte in the line of succession.
Previously, under the ancient rules of male primogeniture, royal sons took precedence over their female siblings, even leapfrogging first-born royal daughters.
But a radical shake-up of the royal succession rules removed discriminatory male bias and came into force in March 2015, affecting babies born after October 28, 2011.
FACTS ABOUT ROYAL BIRTHS
• A team of 23 medical staff was on hand for the birth of Prince George and Princess Charlotte at the private Lindo Wing. A handful of midwives and others led by a consultant obstetrician were in the delivery room, but obstetricians, gynaecologists, surgeons, haematologists and theatre staff were also waiting in the wings in case of an emergency.
• Princess Diana was induced because she could not bear the pressure from the media any longer - and claimed doctors had to find a date that suited Prince Charles and his polo fixtures.
• A restless Prince Philip occupied himself by playing squash while awaiting the arrival of his firstborn.
• The Queen had all her four children - Charles, Anne, Andrew and Edward - at home at Buckingham Palace and Clarence House.
• Princess Elizabeth was born at home by Caesarean section in her grandparents' house in Mayfair, London. She was breech and it was a difficult birth for her mother the Duchess of York.
• It used to be the custom that government ministers and other witnesses were present at royal births to ensure no substitute child had been smuggled in.
• The birth of the Queen's cousin Princess Alexandra on Christmas Day in 1936 was the last occasion that a home secretary was present, meaning the Duchess of Cambridge has been spared such an intrusion.
• Prince Charles's birth was the first time in centuries that there was not a government minister there to witness the arrival of a future heir to the throne.