The actors will swap roles throughout the play's run, which is slated to begin in February, the BBC reported.
Nick Dear is adapting Mary Shelley's 1818 horror story "Frankenstein; or, The Modern Prometheus" for the stage.
"Slumdog Millionaire" filmmaker Boyle previously directed Miller in the 1996 film "Trainspotting."
Cumberbatch is known for his work on TV's "Sherlock" and "Fortysomething."
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