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London (CNN) -- With fanfare fit for a prince, Catherine, Duchess of Cambridge, and husband Prince William welcomed their first child Monday.
The baby boy was born at 4:24 p.m., weighing 8 pounds, 6 ounces. A name has not yet been announced for the child, who is third in line to the throne.
"Her Royal Highness and her child are both doing well," read an official bulletin placed outside Buckingham Palace, where crowds erupted in cheers.
People from all over the world had gathered outside Buckingham Palace to await news of the birth. At least one group of well-wishers brought flowers, champagne and a card for the Duke and Duchess of Cambridge.
The fountains at Trafalgar Square were turned blue.
The Auckland War Memorial Museum in New Zealand is lit blue on Wednesday, July 24, to celebrate the birth of a baby boy to Prince William, the Duke of Cambridge, and Catherine, the Duchess of Cambridge. Catherine gave birth to the boy at 4:24 p.m. July 22. He weighed 8 pounds, 6 ounces. A name has not been announced for the child, who is third in line to the British throne.
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"I'm sure that right across the country and indeed right across the commonwealth, people will be celebrating and wishing the royal couple well," said British Prime Minister David Cameron.
"It is an important moment in the life of our nation, but I suppose above all, it's a wonderful moment for a warm and loving couple who got a brand new baby boy," he said.
The new parents spent some time with their baby before calling family members -- starting with Queen Elizabeth II -- to announce the birth, a Kensington Palace source told CNN royal correspondent Max Foster.
Prince William remained at Catherine's side throughout the labor and the baby was born vaginally, not via a C-section, the source said.
"We could not be happier," said Prince William, according to the Kensington Palace source.
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The royal couple remained in hospital overnight but hopes were high that they'd make an appearance as early as Tuesday.
A multigun salute is set to happen that day to mark the birth.
"Both my wife and I are overjoyed at the arrival of my first grandchild. It is an incredibly special moment for William and Catherine, and we are so thrilled for them on the birth of their baby boy," Prince Charles and wife Camilla said in a statement.
Earlier Monday, the duchess and Prince William traveled by car from Kensington Palace to the Lindo Wing at St. Mary's Hospital.
The hospital, next to Paddington Station in London, is where William and his brother Prince Harry were born.
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The baby's name may be announced when the family leaves the hospital, CNN's Foster reported. Prince William's name was announced a few days after birth, his brother Harry's on departure from hospital.
Some British parents have delayed naming their newborns in recent days in hopes of either copying or avoiding the royal name, he said. British bookmakers favor the names James and George.
The child's title will be His Royal Highness Prince (the baby's name) of Cambridge.
The baby is third in line for the throne now occupied by the queen. Her son, Charles, will succeed her, followed by his son, William.
The queen returned to Buckingham Palace on Monday from Windsor Castle, another of her official residences.
Thanks to a change agreed by the leaders of the Commonwealth countries in 2011 and passed into law this year, the baby's place in the order of succession would have been the same regardless of sex.
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Previously, boys automatically trumped female siblings. So a first-born daughter could be pushed out of line by a younger brother.
The British monarch is also head of state in 15 Commonwealth countries, including Australia, Canada, New Zealand, Belize and Jamaica.
Canadian Prime Minister Stephen Harper offered his country's congratulations.
"The arrival of the newest member of the Royal Family, a future Sovereign of Canada, is a highly anticipated moment for Canadians given the special and warm relationship that we share with our Royal Family," he said in a statement.
Barack and Michelle Obama also gave their best wishes.
"The child enters the world at a time of promise and opportunity for our two nations," the president and first lady said in a statement. "Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince."
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The first child of the Duke and Duchess of Cambridge, Prince William and Catherine, was born on Monday, July 22. Speculation is rife as to what name they will choose for the new heir to the British throne.
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The royal birth is expected to be good for business.
The UK-based Centre for Retail Research estimates retailers will sell $121 million worth of royal-related baby toys and souvenirs. Merchandise ranges from diaper covers and clothing to a "prince potty chair," which of course is in the shape of a throne.
On Twitter, topics related to the royal baby jumped to the top of the trending list in the United Kingdom Monday morning. Worldwide, hashtags such as #RoyalBabyBoy and #Will & Kate were trending later in the day.
Many tweets were along the lines of the comment of Holly Thrift, who wrote, "The royal baby is coming! I am freaking out!"
The baby was the only topic on the radio talk show hosted by Vanessa Feltz on BBC London 94.9 on Monday morning.
But not everyone was thrilled. Feltz read on air a message from "Gary" asking, "Please, please please, I implore you not to devote too much of the morning's show to the royal baby."
Feltz replied, "C'mon, Gary, give an inch. .... It's huge, we can't ignore it."
She reported Gary sent another message: "OK, point taken. I'm a beaten man."
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CNN's Sarah Aarthun and journalist David Simpson contributed to this report.
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Members of the Honourable Artillery Company fire a salute at the Tower of London on Tuesday, July 23, to mark the birth of a son to Prince William and Catherine, Duchess of Cambridge.
People gather outside Buckingham Palace in London on July 23 to read the notice announcing the birth of the royal baby. The news was placed in the forecourt of Buckingham Palace on July 22.
A man reads a copy of British tabloid The Sun, renamed "The Son," on July 23.
Empty bottles of alcohol sit outside Buckingham Palace in London on July 23.
Crew members of the British warship HMS Lancaster celebrate the birth of the royal baby on patrol in the Caribbean in a handout photo released July 23.
A sand sculpture was created by sand artist Sudarshan Pattnaik to celebrate the birth in Puri, India, on July 23.
Crowds push forward to see the birth announcement on Monday, July 22.
People clamor for their chance to see and photograph the birth announcement that was placed on a golden easel by the queen's press secretary on July 22.
The London Eye Ferris wheel on the banks of the Thames is lit up in red, blue and white to mark the birth of the boy on July 22.
The fountains at Trafalgar Square are lit blue to signify the birth of a boy on July 22.
Royal fans celebrate the announcement of the birth of a boy to the Duke and Duchess of Cambridge at St. Mary's Hospital in London on July 22.
Hayley Simmonds, an employee at the British restaurant and grocery Tea & Sympathy, celebrates the birth on July 22 by hanging a sign in the store's window in New York.
Karen Milne, left, of Scotland wears a mask of Catherine, Duchess of Cambridge, as she and friends celebrate the royal birth at Ye Olde King's Head English Pub in Santa Monica, California, on July 22.
Revelers crowd against the railing of Buckingham Palace in London after an official notice proclaiming the birth was put on display on July 22.
Crowds gather outside Buckingham Palace on July 22 after the announcement of the birth.
The queen's press secretary, Ailsa Anderson, left, and Badar Azim, a palace footman, place the official birth announcement on a golden easel in front of Buckingham Palace on July 22.
Crowds gathered outside Buckingham Palace cheer as Anderson places the birth announcement in front of the palace on July 22.
A town crier reads the announcement of the birth outside the Lindo Wing of St. Mary's Hospital in London on July 22.
Two of the gynecologists who attended to the duchess, Marcus Setchell, center, and Alan Farthing, right, leave the Lindo Wing of St. Mary's Hospital on July 22.
Media gather outside the Lindo Wing of St. Mary's Hospital in London on July 22 as they await news of the birth.
Crowds gather outside Buckingham Palace in London as news of Catherine, Duchess of Cambridge's, labor arrives on July 22.
A Buckingham Palace official on July 22 hands the birth announcement to a colleague in a car to be driven from St. Mary's Hospital in London to Buckingham Palace.
Police guard the Lindo Wing at St. Mary's Hospital in London as crowds gather and await news of the birth of the first child of the Duke and Duchess of Cambridge on July 22.
Royal supporters are interviewed by a television crew outside St. Mary's Hospital on July 22.
Crowds gather behind a barricade outside St. Mary's Hospital as they wait for news of the birth on July 22.
Hospital staff look out over a gathering crowd at St. Mary's Hospital in London on July 22.
Royal fan Teba Diatta stands outside St. Mary's Hospital with a cake decorated for the occasion on July 22.
Royal supporter Margaret Tyler holds decorative balloons as she waits outside St. Mary's Hospital in London on Saturday, July 20.
The British royal family tends to opt for very traditional names, often referencing monarchs of the past. Queen Elizabeth II is seen here in 1951 with Prince Philip, and a young Prince Charles and Princess Anne.
George is the current front-runner should the new baby turn out to be a boy. There have been six previous King Georges, the most recent being the current queen's father -- though he was known by friends and family as Bertie.
In recent years some minor royals have moved away from "regal" to more fashionable modern choices. Queen Elizabeth II's grandson Peter Phillips and his wife Autumn named their daughters Savannah and Isla.
British bookmakers also took bets on some more unusual names, including Alberta, perhaps in recognition of the Duke and Duchess's hugely successful trip to Canada in 2011.
You can even wager -- at odds of 500/1 -- that William and Kate will name the royal baby Elvis, after a monarch of a completely different kind: the "King of Rock 'n' Roll," Elvis Presley.
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