The couple smiled proudly as they took turns holding the baby, who was swaddled in a blanket, and briefly introduced him to the reporters, photographers and well-wishers gathered outside the hospital.
Kensington Palace confirmed earlier in the day the tiny prince would be going home with his parents Tuesday night.
The child is the first for Kate and William, the grandson of Britain's Queen Elizabeth II.
William, who said he had changed his first "nappy," told the crowd outside the hospital Tuesday evening, "We're still working on a name. ... He has her looks, thankfully."
"It's such a special time," a radiant Kate said on the steps of the hospital.
The new dad also revealed: "He's got a good pair of lungs, that's for sure. He's a big boy. He's quite heavy."
The baby is third in line for the British throne behind his father and grandfather, Prince Charles.
The newest addition to the royal family was born Monday afternoon after 14 hours of labor and a natural delivery.
The Guardian said William spent Monday night with his wife and newborn son in the hospital's luxurious Lindo wing.
"We would like to thank the staff at the Lindo wing and the whole hospital for the tremendous care the three of us have received," the couple said in a statement Tuesday morning. "We know it has been a very busy period for the hospital and we would like to thank everyone -- staff, patients and visitors -- for their understanding during this time."
The BBC said Charles and his wife Camilla, as well as Kate's parents, Carole and Michael Middleton, visited the newborn in the hospital Tuesday afternoon.