George Alexander Louis, known as Prince George of Cambridge, was born Monday to Harry's brother Prince William and William's wife Kate.
Harry talked about the latest addition to the royal family at a photographic exhibition in London documenting the work of his Africa-based charity Sentebale Thursday.
Asked what he plans to accomplish as George's uncle, Harry told the BBC: "To make sure he has a good upbringing, and keep him out of harm's way and to make sure he has fun. The rest I'll leave to the parents. ...
"I only hope my brother knows how expensive my babysitting charges are."
Harry said it is "fantastic to have another addition to the family" and when he met the newborn he "was crying his eyes out."
Harry is now fourth in line for the British throne behind his father Prince Charles, brother William and nephew George.