Tony Cacciotti, Chase Mishkin, David Steiner and Leonard Soloway made the announcement Thursday.
The play was written by Matthew Lombardo and directed by Rob Ruggiero.
Previews are to begin Feb. 19 and opening night is set for March 14 at Manhattan's Lyceum Theatre.
"'Looped' tells the story of Tallulah Bankhead, the internationally celebrated actress, being called into a sound studio in 1965 to re-record -- or 'loop' -- one line of dialogue for what would be her last film -- the dreadful 'Die, Die My Darling,'" the producers said in a news release. "Southern, but by no means a belle, Ms. Bankhead was known for her wild partying and convention-defying exploits that outshone even today's celebrity bad girls. And given her inebriated state -- and inability to loop the line perfectly -- what ensues is a hilarious showdown between an uptight and conservative sound editor, Danny Miller, and the outrageous legend."
Best known for her work on TV's "Valerie," "Rhoda" and "The Mary Tyler Moore Show," Harper was last seen on Broadway in "The Tale of the Allergist's Wife."
She originated the role of Tallulah in the world premiere production of "Looped" at the Pasadena Playhouse, and has reprised the role at the Cuillo Centre and at Arena Stage.