The 39-year-old Cooper, who has been nominated in the best supporting actor category at the Oscars for his role in 'American Hustle', was last on Broadway opposite Julia Roberts and Paul Rudd for 2006 play 'Three Days of Rain'.
In 'The Elephant Man' Cooper will play the role of John Merrick, a severely deformed and soulful figure, reported Entertainment Weekly.
'The Elephant Man' hasn't been performed on Broadway since 2002.
The role of Merrick has been memorably played by John Hurt in David Lynch's 1980 film adaptation.