Tony Award-winner Bob Crowley will design the sets, Ann Roth will do the costume design and Jean Kalman will handle lighting.
The show will begin previews on March 6 and open on March 29, 2007, at the Booth Theatre.
Redgrave, who has a lifetime of theatre experience, both in London and New York, most recently appeared on Broadway in Long Day's Journey Into Night. She won a Tony Award for her performance as Mary Tyrone.
The piece will be a one-person show. "The Year of Magical Thinking" was published in October 2005 by Knopf. The book is a searing narration of a trying year in Didion's life, beginning with the heart attack that felled her husband, John Gregory Dunne, on Dec. 30, 2003. Their only child, Quintana Roo Dunne Michael, died in August 2005, after the book had been written.
Quintana had been hospitalized with the flu and then fell into septic shock just before Dunne's death. She later died of abdominal infections and other illnesses, the Times said. She was 39 years old.
Didion's books include "Play It as It Lays" and "Slouching Toward Bethlehem." She has also written, in collaboration with Dunne, several screenplays, including "The Panic in Needle Park," "A Star Is Born" and "Up Close and Personal."
Playwright Hare is the author of dozens of plays including Plenty, Skylight, Amy's View, The Blue Room and the one-person show Via Dolorosa, in which he starred.