London (CNN) -- They looked like "a normal couple" as they left the hospital, one bystander said.
Of course, most normal couples don't have a crowd of reporters, photographers and random well-wishers waiting for them to show off their new baby.
Prince William and Catherine, the Duchess of Cambridge, emerged from St. Mary's Hospital in London on Tuesday evening to give the public its first view of the new heir to the British throne, joking that the still-unnamed boy had more hair than his father. Catherine and William took turns holding the child, wrapped in a cream-colored blanket, as they waved to well-wishers outside.
The couple is "still working on a name," William said, "so we'll have that as soon as we can." But he added, "He's got her looks, thankfully."
The prince has already changed his first diaper, the couple told reporters.
"It's very emotional. It's such a special time," Catherine said.
The couple left the hospital Tuesday evening, with William carrying the boy out in a car seat and installing him in the back of a black SUV. Then he got behind the wheel for the trip to their residence at Kensington Palace.
On their way out, they walked out down the same steps where Diana, Princess of Wales, and Prince Charles gave the world its first look at Prince William 31 years ago.
"It was so exciting. It was fantastic," said Eliza Wells, one of those gathered outside the hospital. "The crowd erupted, because everyone's been waiting so long for it."
William and Catherine "both seemed very relaxed, even with the press there and the crowd," Wells said. "They just seemed like a normal couple."
Shortly before the departure, Charles stopped by for a brief visit with his first grandchild, accompanied by his wife, Camilla, the Duchess of Cornwall. He told reporters it was "marvelous."
And Catherine's parents, Carole and Michael Middleton, visited earlier, with Carole Middleton telling reporters the royal baby is "absolutely beautiful."
She said both mother and baby are doing "really well" and that she and her husband were "so thrilled" at being grandparents.
Bells, gun salutes
The 8-pound, 6-ounce boy was born Monday afternoon. He's third in line, behind Charles and William, for the British throne now held by his great-grandmother, Queen Elizabeth II.
Tuesday, London echoed with the sound of cannonades and music to mark the birth.
Guardsmen at Buckingham Palace, the queen's residence, played the Cliff Richard song "Congratulations" at the Changing of the Guard. The military ceremony, much beloved by tourists, involves a new guard exchanging duty with the old guard in the palace forecourt.
The King's Troop Royal Horse Artillery in Green Park fired 41 shots in tribute to the boy, while the Honorable Artillery Company at the Tower of London fired 62 rounds.
At the same time the bells of Westminster Abbey, where William and Catherine were married in April 2011, began to peal, in keeping with royal tradition, and were set to continue for more than three hours.
The news of the boy's birth, announced about four hours after the event Monday, prompted cheers and celebration among the crowds of well-wishers outside Buckingham Palace. At least one group of well-wishers brought flowers, champagne and a card for the Duke and Duchess of Cambridge.
Social media networks were also abuzz with the news, which made headlines around the world.
'We could not be happier'
The new parents spent some time with their baby before calling family members -- starting with the queen -- to announce the birth, a Kensington Palace source told CNN royal correspondent Max Foster.
"We could not be happier," said Prince William, according to the Kensington Palace source.
Prince William remained at Catherine's side throughout the labor, and the baby was born naturally. An official bulletin was placed on a gilded easel outside Buckingham Palace.
The celebrations for the arrival of the new prince -- whose title will be His Royal Highness Prince (the baby's name) of Cambridge -- were hard to miss in the capital.
The fountains at Trafalgar Square were dyed blue; the BT Tower, a London landmark, flashed the words "It's a boy;" and the London Eye was illuminated in patriotic red, white and blue.
Farther afield, Canada -- where the British monarch is head of state -- turned its side of the Niagara Falls blue to mark the birth, and the CN Tower in Toronto was lit up the same color.
Betting on a name
It was a long wait for the media camped outside St. Mary's Hospital, but when the news of the birth finally came, the excitement of the moment was huge.
The Sun newspaper, Britain's best-selling tabloid daily, changed its masthead Tuesday to "The Son" to mark the occasion, above a picture of the official birth announcement, while the Daily Express and Telegraph emblazoned "It's a boy" across their front pages.
Recognizing that excitement over the prince's arrival is not universal, the Guardian newspaper's website lets users switch to a royal baby-free version of the home page. The front page of UK satirical magazine Private Eye simply says: "Woman has baby."
Many bets are being placed as the wait continues for the baby's name to be announced. British bookmakers Ladbrokes have James as favorite, followed by Henry and George, Philip, Alexander and Richard.
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.
The official British Monarchy Twitter feed said: "The Queen and Prince Philip are delighted at the news of the birth of The Duke and Duchess of Cambridge's baby."
Charles Spencer, brother of the late Diana, Princess of Wales, welcomed the birth of the baby. "We're all so pleased: it's wonderful news," he said in a statement.
"My father always told us how Diana was born on just such a blisteringly hot day, at Sandringham, in July 1961. It's another very happy summer's day, half a century on."
British Prime Minister David Cameron said, "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."
Tributes around the world
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 on the birth of a future king.
"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 U.S. 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."
Russia's President Vladimir Putin and Japan's Prime Minister Shinzo Abe also sent their congratulations.
On Twitter, topics related to the royal baby jumped to the top of the trending list in the United Kingdom on Monday morning. Worldwide, hashtags such as #RoyalBabyBoy and #Will & Kate were trending later Monday.
In a nod to modern times, Clarence House called for people to send news and images of any other new arrivals using the hashtag #WelcometotheWorld.
CNN's Atika Shubert, Dana Ford, Sarah Aarthun, Zarifmo Aslamshoyeva, Susannah Palk and Alla Eshchenko, and journalist David Simpson contributed to this report.