The supernatural tale centres on a man whose life changes forever when he realises that a mysterious boy is causing the deaths of people he loves, according to The Hollywood Reporter.
'Bad Little Kid' was released as an e-story in Germany and France on March 14. King says he wrote it specifically for his fans in those European countries who were so hospitable to him when he visited in November.
Bouzereau, who is also planning on directing 'Bad Little Kid', has a resume packed with making-of documentaries. He wrote and directed the 2011 TCM film 'A Night at the Movies: The Horrors of Stephen King', which featured King discussing horror films and their popularity with moviegoers.
More than 50 of Kings' books and short stories have been adapted into films over the years, including 'The Shining', 'Carrie' and 'The Green Mile'.
An adaptation of the apocalyptic thriller 'Cell' starring Samuel L Jackson is currently in post-production, and Blumhouse produced a film called 'Mercy', an adaptation of King's short story Gramma.