The ceremony will take place May 18 at the Marriott Marquis Times Square.
This year's award nominees will be announced April 24 at Sardi's, a restaurant in Manhattan's theater district.
"We are thrilled to have Stockard and John hosting the best party on Broadway," Drama League Executive Director Gabriel Shanks said in a statement. "With two of New York's brightest stars at the helm, the afternoon will be a joyful and unforgettable celebration of this season's excellence."
Channing can currently be seen in the Broadway hit "Other Desert Cities." Her work in "The Lion in Winter,""House of Blue Leaves," "Four Baboons Adoring the Sun" and "Six Degrees of Separation" earned her four Tony Award nominations.