The 68-year-old star of "The Lord of the Rings" and "X-Men" trilogies will also appear in select performances of Chekhov’s "The Seagull," playing in repertory with "Lear" for a limited engagement, starting Friday.
"Les Miserables" and "Cats" director Trevor Nunn is helming the Royal Shakespeare Company productions in their U.S. premieres.
"Both plays explore the fear that one generation has of another,” Nunn said of "King Lear" and "The Seagull."
"The characters in both plays are confused and frightened by their mortality. Both plays seem to believe that the idea of endurance is more important than any other human belief. It is necessary to endure."
McKellen and Nunn previously collaborated on productions of "Macbeth" and "Othello."
After the BAM run concludes Sept. 30, McKellen and the rest of the troupe will take the shows to the Guthrie Theatre in Minnesota, then to Los Angeles' Royce Hall.
The productions will return to London for a West End engagement at the New London Theatre, starting Nov. 12.