Kate, the wife of Prince William, gave birth to a boy at a hospital in London on Monday, the third child for the British royal couple and now fifth in line to the throne.
Kensington Palace said the baby was born at 1001 GMT and weighs 8 lbs. 7oz. (3.8 kg). William was present for the birth at St Mary's Hospital in west London where their other two children, George and Charlotte, were also born, it added.
"Her Royal Highness and her child are both doing well," the Palace said.
Queen Elizabeth, Prince Charles, the baby's grandfather, and other members of the royal family and Kate's family have been informed and "are delighted with the news," it added.
The baby is the queen's sixth great-grandchild and is behind his siblings George, 4, and Charlotte, 2, their father William, and grandfather and heir Prince Charles in line to the throne.
A 2013 change to the law means that for the first time in British history, a new prince will not supplant his older sister in the order of succession. Previously younger males would take precedence over older female siblings.
William's younger brother Harry, who marries U.S. actress Meghan Markle next month, falls to sixth on the list.
Kensington Palace said the name of the new royal would be announced in due course. Bookmakers have made Albert, Arthur, Jack and Fred the favorite names for a boy.
The official announcement of the birth was made by placing a notice on an easel in the forecourt of the queen's London home, Buckingham Palace, a tradition that has been in place since it became the sovereign's official residence in 1837.
"My warmest congratulations to the Duke and Duchess of Cambridge on the birth of their baby boy," Prime Minister Theresa May said. "I wish them great happiness for the future."
William and Kate met as students at St Andrews University in Scotland. They wed in a pageant-packed ceremony at Westminster Abbey in April 2011 and are treated as global celebrities.
The couple now live at Kensington Palace and last year William gave up his day job as an air ambulance pilot to concentrate full time on royal duties on behalf of his grandmother, having faced some criticism from British newspapers who dubbed him "workshy Wills."
He has been determined to play a hands-on role in bringing up his children while also protecting their privacy, an issue close to his heart after the death of his mother, Princess Diana, in a 1997 Paris car crash as her limousine sped away from chasing paparazzi.
"I think he takes on a lot more engagements than he used to," said royal biographer Claudia Joseph.
"But compared to members of the general public who have full-time jobs, he still has some time off to look after the children, to give them their baths, to put them to bed and I think he'll continue to do that," Joseph said.
The British royals are rarely out of the media glare, but the baby arrives at a time when the Windsors have particularly been in the limelight.
On Saturday William joined the queen and other senior royals, with the exception of Kate, as the monarch celebrated her 92nd birthday at a televised concert.
The queen also played a prominent role at the Commonwealth Heads of Government meeting in London last week, where it was announced that Charles would succeed her as head of the network of mainly former British colonies.
While interest in their third child has been more muted than with the birth of their first, large numbers of photographers and broadcasters from around the globe massed outside the hospital, along with some dedicated royal fans.
"We've been coming out doing this for 21 years," said John Loughrey, 63, from south London, who was wearing a Union Jack onesie and hat and holding a baby doll adorned with a crown. He said he had been camped outside the hospital for 15 days.
"We were here for George and Charlotte and we'll be there for the royal wedding too," he said, referring to Harry and Markle.
However, not everyone in Britain is so enamored.
"The arrival of a new prince or princess highlights the unfairness of the hereditary principle—for the millions of children told they'll never be good enough and for the baby whose life has been predetermined," anti-monarchist group Republic said.
"The absurd media speculation ignores these serious questions while showing us the kind of intrusion the royal baby can expect for the rest of its life."
One consequence of the birth is that some existing members of the royal family are pushed to the periphery, and this has led to calls for the monarchy to be pared down.
"One of the problems all members of the royal family have is they start quite close to the throne and gradually as time goes on they go further and further away," royal historian Hugo Vickers said.
"It's very easy to talk about a bloated royal family but it's not really fair because the queen has an enormous amount of requests of things to do and her family are there to support her."
The birth also gives Kate's own family another cause for celebration after it was reported by British media on Sunday that her sister Pippa was pregnant with her first child.
Get Spirit-filled content delivered right to your inbox! Click here to subscribe to our newsletter.
Join us on our podcast each weekday for an interesting story, well told, from Charisma News. Listen at charismapodcastnetwork.com.
Great Resources to help you excel in 2019! #1 John Eckhardt's "Prayers That..." 6-Book Bundle. Prayer helps you overcome anything life throws at you. Get a FREE Bonus with this bundle. #2 Learn to walk in the fullness of your purpose and destiny by living each day with Holy Spirit. Buy a set of Life in the Spirit, get a second set FREE.