The Tony Award-winning drama was written by Peter Morgan, author of the films "The Queen" and "The Last King of Scotland."
The role of famous British talk-show host David Frost in the national tour production of "Frost/Nixon" has not yet been cast, representatives for the show said.
Michael Grandage, who directed the original London and Broadway productions, is expected to direct the tour, to begin this fall.
Keach has starred in numerous stage productions in the past and is well-known for his portrayal of detective Mike Hammer on television.
He also starred in the the title role of the miniseries "Hemingway" and recently appeared in the sit-com "Titus."
Keach's film credits include "The Heart is a Lonely Hunter," "The Traveling Executioner," "The New Centurions," "Doc," "Fat City," "The Longriders," "That Championship Season," "Roadgames," "Escape from LA" and "American History X."