Wright joins the previously announced E. Faye Butler.
The Broadway League had decided not to dim Broadway's marquees for the pioneering comedian.
Hadary will star as Tevye in the D.C. theater's production of Fiddler on the Roof.
High school competitors will make their Broadway debut on the stage of the August Wilson Theatre.
New plays by Morris Panych and Katori Hall are also on tap for the Washington, D.C. mainstay.