The outgoing 'Doctor Who' star, who will bow out of his BBC1 role as the Timelord in the 2013 Christmas special, will sing on stage in the reworking of the controversial Bret Easton Ellis novel.
Published in 1991, the novel sparked calls for it to be banned and it was criticised for being misogynistic and for its graphic scenes of violence but went on to become a cult classic.
In 2000, Hollywood actor Christian Bale played Bateman, the book's narrator and wealthy, psychopathic New York investment banking executive who embarks on a killing spree, in the 'American Psycho' film.
The musical thriller runs from December 3 to January 25 at London's Almeida Theatre and could transfer to the West End and Broadway.
Smith, who previously appeared on stage in 'The History Boys', will next be seen in 'Doctor Who' next month, in the 50th anniversary episode which will be followed by the Christmas special.
His co-stars in the musical include Ben Aldridge, Charlie Anson, Jonathan Bailey, Katie Brayben, Cassandra Compton, Holly Dale Spencer, Susannah Fielding, Simon Gregor, Holly James, Lucie Jones, Tom Kay, Gillian Kirkpatrick, Eugene McCoy and Hugh Skinner.
The stage production will be directed by Rupert Goold, the Almeida's artist director, with a book by Roberto Aguirre-Sacasa and music and lyrics by Duncan Sheik.