London (CNN) -- All eyes are glued Tuesday to the hospital where Catherine, Duchess of Cambridge, and husband Prince William welcomed their first child as a joyful public waits for its first glimpse of the new royal heir.
The couple will leave St. Mary's hospital Tuesday evening with the boy, who was born Monday, Kensington Palace said. A name has not yet been announced for the child, who is third in line to the British throne.
The royal baby was born at 4:24 p.m. Monday, weighing 8 pounds, 6 ounces. The new parents remained in the private Lindo Wing of St. Mary's Hospital in London overnight.
They could appear holding their son on the same steps where Diana, Princess of Wales, and Prince Charles gave the world its first sighting of Prince William 31 years ago. Charles came to the hospital for a brief visit with his first grandchild Tuesday evening, accompanied by his wife Camilla, the Duchess of Cornwall. He told reporters it was "marvelous."
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.
William and Catherine thanked hospital staff "for the tremendous care the three of us have received" in a statement issued via Kensington Palace.
"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," they said.