Written by playwright Rupert Holmes, the show is to open Oct. 20 at the John Golden Theatre, producers Daryl Roth and Eva Price said Tuesday.
It will be the first Grisham property adapted for the stage.
Ethan McSweeny is to direct the production, with previews beginning Sept. 28.
Additional information, including the complete casting and creative team, will be announced shortly, the producers said.
"For almost a quarter of a century, 'A Time to Kill' has captivated readers with its raw exploration of race, retribution and justice," Grisham said in a statement.
"It was my first book and the first that I have allowed to be adapted for the theater. Rupert Holmes did an excellent job of translating it from the page to the stage, and I am happy that not only my loyal readers, but a whole new audience will be able to experience this story in live theater."
"John Grisham's endlessly gripping, perfectly-plotted storytelling is so well-suited for the live theater, and we are thrilled to be bringing this first-ever stage adaptation of one his novels to Broadway," Roth and Price said in a joint statement.
"Rupert Holmes has written an adaptation that masterfully replicates for theatergoers the page-turning thrill of reading a Grisham novel, while also honoring the powerful intimacy of its exploration of the injustices of our not-so-distant past."