The drama, written by Thelma & Louise scribe Callie Khouri, focuses on two musicians - one is already famous, while another is about to hit the big time.
Close has now joined the cast of the project, TV Line says.
He will play the husband of the musician who is already known to the public.
Close has previously starred in shows such as Without A Trace and Chaos. He also recently appeared in American Horror Story.
News of his casting comes after Heroes star Hayden Panettiere signed up to play the rising star in Nashville.
Other actors who have already joined the project include Sam Palladio, Powers Boothe, Jonathan Jackson and Robert Wisdom.