The Oscar winner will also serve as an executive producer on the project.
The one-hour drama will examine some of "history's most impactful and world-changing decisions ... made by America's charismatic, complex, and dynamic First Ladies," according to Showtime.
The network also said the series "will peel back the curtain on the personal and political lives of our most enigmatic heroes."
The first season will focus on Obama, Eleanor Roosevelt and Betty Ford. Additional casting for the series has not yet been announced.
The series, which has received a three-script commitment from Showtime, will be written by author Aaron Cooley.
There's no word yet on when the show will premiere. In the meantime, the final season of Davis' ABC drama, "How to Get Away with Murder," begins Sept. 26.