To huge cheers from well-wishers and hospital staff, the beaming couple waved and took turns to hold their son, wrapped tightly in a white blanket with only the top of his head visible.
Kate, 31, gave birth to the couple's first child on Monday afternoon, ending weeks of feverish anticipation about the arrival.
They adhered to tradition by giving the public the first sight of the baby on the steps of the hospital as they left.
The baby is third in line to the throne after grandfather Charles and William, 31, and pushes the fun-loving Prince Harry, William's brother, into fourth place.
Congratulations flooded in from around the world after the announcement of the birth, which was followed moment-by-moment by global media.
Royal baby had triggered a frenzy among the waiting reporters and camerapersons.
Hordes of TV crews, photographers and royal fans wrapped in British flags were camped outside the hospital for the first glimpse of the baby.
To mark the birth, the Royal Artillery fired a 41-gun salute at London's Green Park and 62 rounds were fired at the Tower of London.
The couple will eventually take up residence with their baby at Apartment 1A in London's Kensington Palace.
Britain's Prince William holds his baby son outside the Lindo Wing of St Mary's Hospital.
Britain's Prince William and his wife Catherine, Duchess of Cambridge appear with their baby son outside the Lindo Wing of St Mary's Hospital.