"My absolute dream come true," the Emmy-winning actress tweeted in response to her casting.
Lila Neugebauer is directing the Second Stage Theater production, which will begin previews June 19 at the Tony Kiser Theater. An official opening date has been set for July 12.
"The title character is portrayed by five actresses at different points in her life," a news release explained. "Casting of the additional actresses will be announced shortly."
Second Stage Theater previously produced the New York premiere of Letts' play Man from Nebraska last winter.