The royal couple appeared 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.
She 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 prince said they are still determining what to name the baby.
The couple re-entered the hospital to place the child in a car seat before re-emerging to get into an SUV. William drove the couple away -- palace officials said they will head to an apartment in Kensington Palace.
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 appearance three decades ago, when Princess Diana and Prince Charles carried the newborn William out to pose for photographs on the same steps in 1982.
Earlier, grandparents Prince Charles, his wife, Camilla, and Michael and Carole Middleton -- Kate's parents -- were the first relatives to visit the young family at the hospital.
Charles called the baby "marvelous," while a beaming Carole Middleton described the infant as "absolutely beautiful."
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 excited applause by hundreds of Britons and tourists gathered outside the hospital 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.
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