The play is slated to open in New York in September 2008.
Radcliffe, 18, is best-known for starring in the "Harry Potter" film franchise. However, he made headlines earlier this year when he appeared naked as part of his role in a staging of "Equus" at London's Gielgud Theatre.
Radcliffe told BBC News he was happy to play the part again in New York.
"Of course there's nerves. If I wasn't nervous, then I would be dead," Radcliffe said. "It's a good thing, it's healthy. I'm obviously nervous, but I'm very, very excited."
The actor told the BBC he hopes the story of a troubled young man who blinds horses will be well-received in New York.
"If we can get a straight play to really succeed in a world of theater that is so besieged by musicals, that would be a real achievement and I think the time is absolutely right to do it there," he said. "All the people I know in New York say New York is ready for this kind of play."