Rowling will "collaborate closely" with the project, with the number of episodes yet to be determined.
The Casual Vacancy was released in September to mixed reviews, but became a global best-seller - topping one million copies sold in English in all formats across all territories.
"I always felt that, if it were to be adapted, this novel was best suited to television and I think the BBC is the perfect home," she said.
BBC One controller Danny Cohen added: "It is thrilling to be bringing the work of JK Rowling to BBC One audiences. JK Rowling's story-telling is of course peerless in its popularity, and I am looking forward to collaborating with her.
"This project highlights the ambition and scale of BBC One Drama, as well as the ability of modern television to attract the world's biggest talent and most exciting creative ideas."
> JK Rowling's The Casual Vacancy tops fiction chart
> JK Rowling: 'Next book will be for kids'