Parsons is the star of TV's "The Big Bang Theory." He made his Broadway debut in Larry Kramer's 2011 Tony Award-winning play "The Normal Heart" and was honored with the rest of the cast of that show with the Drama Desk Award for Outstanding Ensemble Performance.
Co-starring Jessica Hecht and Charles Kimbrough, "Harvey" is to begin previews May 18, with opening night set for June 14 at Studio 54 in Manhattan. The limited engagement is scheduled to run through Aug. 5.
The Roundabout Theatre Company production of Mary Chase's play will be directed by Scott Ellis.
"Harvey" first played the Broadway stage in 1944 and was directed by Antoinette Perry. It won the Pulitzer Prize for drama in 1944, and its initial run lasted for four years -- 1,775 performances. James Stewart assumed the role of Elwood from Frank Fay in the 1944 production and played the role in the 1970 production as well as the film adaptation in 1950. Helen Hayes played Veta opposite Stewart in the 1970 production.
In the new production, Parsons will play Elwood and Hecht will play Veta.
"Charming and kind, Elwood has only one character flaw: an unwavering friendship with a 6-foot-tall, invisible white rabbit named Harvey. In order to save the family's social reputation, Elwood's sister Veta takes Elwood to the local sanatorium. But when the doctors mistakenly commit his anxiety-ridden sister, Elwood -- and Harvey -- slip out of the hospital unbothered, setting off a hilarious whirlwind of confusion and chaos as everyone in town tries to catch a man and his invisible rabbit," a synopsis said.