Costner will play Brooks -- a tortured man who tries to stay in control -- while Hurt, nominated for a 2006 Academy Award for "A History of Violence," will play his evil alter ego, The Hollywood Reporter said.
The script was co-written by Bruce Evans, who will also direct the thriller.
Hurt won his Oscar for "Kiss of the Spiderwoman" in 1985.
"Mr. Brooks" is expected to start filming in Louisiana next month.
Notable deaths of 2014 [PHOTOS]