Redgrave, who was most recently on the New York stage in Jesse Eisenberg's The Revisionist, will star opposite Kelly Reilly in the 13-episode series penned by Amy Holden Jones.
"The Black Box," according to Deadline.com, centers on "Elizabeth Black (Reilly), a world-renowned neuroscientist who appears to have it all but is constantly haunted by her own struggle with mental illness. And that is not the only secret she’s kept locked away from her family and her new fiancé."
Redgrave has been cast as Dr. Hartramph, Elizabeth’s psychiatrist who knows all her secrets.
Simon Curtis is directing the series, which will likely air in 2014. Executive producers include writer Jones; Ilene Chaiken, who is also the showrunner; Bryan Singer; 3 Arts’ Oly Obst; and Anne Thomopoulos.
Redgrave's more recent TV credits include "Playhouse Presents," "Call the Midwife," "Political Animals" and "Nip/Tuck."