The ecommerce company signed on Allen last January to write a show about whatever he wanted.
Although Allen confessed to struggling with ideas back in May, causing him to regret his decision to sign on with Amazon, he now plans to begin shooting a 1960s-rooted show starring Cyrus and Elaine May in March.
Although Amazon has released a handful of original television shows, its two biggest have been "Transparent" and "Mozart in the Jungle," both of which won Golden Globes. Cyrus' high-profile hire can't promise anything about the quality of Allen's show, though it will likely help attract eyeballs.
Amazon uses its TV and movie streaming service to help drive sign-ups and renewals for its Prime shopping subscription program. The company spent an estimated $3 billion last year on its streaming music and video services.
Disclosure: Jeff Bezos is an investor in Business Insider through hispersonal investment company Bezos Expeditions.