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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.

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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 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.