The announcement was made by Jeffrey Richards, Jerry Frankel and Louise Gund.
Rehearsals are to begin Jan. 14, with previews beginning Feb. 10, and an opening night set for March 6. It is directed by Bill Rauch, artistic director of Oregon Shakespeare Festival.
"'All the Way is a gripping new play about a pivotal moment in American history," a synopsis said. "This drama will take audiences behind the doors of the Oval Office and inside the first years of Lyndon B. Johnson's presidency, and his fight to pass a landmark civil rights bill."