The royal couple, both 31, looked happy and relaxed as they waved at the crowds of journalists and onlookers gathered outside London's St. Mary's Hospital, posing for photographs and joking with reporters.
Kate, wearing a baby blue polka dot Jenny Packham dress, smiled and waved as she stepped out from the hospital doors with the future monarch in her arms.
"It's very emotional. It's such a special time. I think any parent will know what this feeling feels like," she told journalists.
Kate then gave the baby to her husband, who, cradling their child, said: "He's got her looks, thankfully. He's got a good pair of lungs on him, that's for sure."
William added: "He's a big boy. He's quite heavy," and laughed when a reporter asked him about the baby's hair.
"He's got way more than me, thank God," he said.
The couple also revealed that William has had a go at changing the infant's first diaper. "He's very good at it," Kate said.
The new parents drew whoops and excited applause from well-wishers as they revealed the newest member of Britain's royal family. William said they're still trying to decide what to name the little prince.
The couple re-entered the hospital to place the child in a car seat before re-emerging to get into an SUV. William drove them away — palace officials said they will head to an apartment in Kensington Palace and spend the night there.
The young family's first public appearance together has been the moment that the world's media and crowds of onlookers camped outside the hospital had long been waiting for, and the photographs snapped Tuesday are likely to be reprinted for decades as the baby grows into adulthood and his role as a future king.
The appearance recalls a similar one three decades ago, when Princess Diana and Prince Charles carried a newborn William out to pose for photographs on the same steps in 1982.
Katie Allan, 26, was elated to witness the 2013 edition. "William gave us a wave as they drove away so it was perfect. Days like this really bring the country together," she said.
Earlier, William's father, Charles, and his wife, Camilla, as well as Michael and Carole Middleton — Kate's parents — visited the young family at the hospital.
Charles called the baby "marvelous," while a beaming Carole Middleton described the infant as "absolutely beautiful."
It was not immediately clear when Queen Elizabeth II would meet the newborn heir.
The couple's Kensington Palace office said Kate, the Duchess of Cambridge, gave birth to the 8 pound, 6 ounce (3.8 kilogram) baby boy at 4:24 p.m. Monday.
The news was greeted with shrieks of joy and applause by hundreds of Britons and tourists gathered outside the hospital's private Lindo Wing and Buckingham Palace.
Revelers staged impromptu parties at both locations, and large crowds crushed against the palace gates to try to catch a glimpse — and a photograph — of the golden easel placed there to formally announce the birth.
Hundreds were still lining up outside the palace gates Tuesday to get near the ornate easel.
In London, gun salutes were fired, celebratory lights came on, and bells chimed at Westminster Abbey, where William and Kate wed in a lavish ceremony that drew millions of television viewers worldwide.
Canada also saluted the birth of the baby who is 3rd in line to be king of Canada. On Parliament Hill, there was a 21-gun salute Tuesday and on Monday night, several landmarks, including the CN Tower, Niagara Falls and the Peace Tower in Ottawa, were bathed in blue in honour of the baby boy.
Elsewhere, royalist group Monarchy New Zealand said it had organized a national light show, with 40 buildings across the islands lit up in blue to commemorate the royal birth, including Sky Tower in Auckland, the airport in Christchurch, and Larnach Castle in the South Island city of Dunedin.
The baby is just a day old — and may not be named for days or even weeks — but he already has a building dedicated to him.
Australian Prime Minister Kevin Rudd said an enclosure at Sydney's Taronga Park Zoo would be named after the prince as part of a gift from Australia. The government would donate 10,000 Australian dollars ($9,300) on the young prince's behalf toward a research project at the zoo to save the endangered bilby, a rabbit-like marsupial whose numbers are dwindling in the wild.
British media joined in the celebration, with many newspapers printing souvenir editions.
"It's a Boy!" was splashed across many front pages, while Britain's top-selling The Sun newspaper temporarily changed its name to "The Son" in honour of the tiny monarch-in-waiting.
The birth is the latest driver of a surge in popularity for Britain's monarchy, whose members have evolved, over several decades of social and technological change, from distant figures to characters in a well-loved national soap opera.
"I think this baby is hugely significant for the future of the monarchy," said Kate's biographer, Claudia Joseph.
For some, though, it was all a bit much.
"It's a baby, nothing else," said Tom Ashton, a 42-year-old exterminator on his way to work. "It's not going to mean anything to my life."
Associated Press writers Gregory Katz, Paisley Dodds, Maria Cheng and James Brooks in London, Rod McGuirk in Canberra, Australia, and Kristen Gelineau in Sydney, Australia, contributed to this report.
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