The 37-year-old actor will appear in the role as part of the second season of BBC Two's Shakespeare's History plays, reported Variety online.
'Richard III' is part of a series of Shakespeare's plays, which also includes 'Henry VI' in two parts.
Dominic Cooke, who was artistic director of the Royal Court Theater from 2007 to 2013, will direct all three films.
"I can't wait to work with Dominic Cooke again to bring this complex, funny and dangerous character to life," Cumberbatch said.