The royal couple, who had travelled back to London from an official engagement in Yorkshire, were beaming as they stepped out of the car to rapturous applause and cheers from the gathered crowds.
It will be the first time that the new first, second and third in line to the throne are in the same room.
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The Duke and Duchess of Cornwall waved to the crowds before warmly greeting the hospital staff who had welcomed the heir into the world.
The grandfather looked thrilled to be visiting his first grandchild. "You've had a long wait," he joked to the reporters in the press pen.
It was the little Prince's second visit on Tuesday afternoon from grandparents.
Michael and Carole Middleton had visited earlier in the day. They were delighted as they spoke to members of the press about the new family's progress.
"He's absolutely beautiful," Carole said. "They're doing fabulously."
During Charles and Camilla's two-day visit to Yorkshire, they were bombarded with questions from journalists and well-wishers alike about the progress of the royal baby.
On Tuesday morning, Camilla revealed that she thinks her husband will have a "wonderful time" being a grandfather.
"It's very exciting and it's wonderful for the grandfather," she added, pointing in the direction of Prince Charles.
"He's brilliant with children, so he'll have a wonderful time."
When the news of the birth of William and Kate's little boy was announced on Monday evening, Prince Charles expressed his joy at becoming a grandfather.
The Prince of Wales said he was "enormously proud and happy" about the birth of his grandson.
"Both my wife and I are overjoyed at the arrival of my first grandchild," his statement read. "It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy.
"Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."