The new series is from Tina Fey and Robert Carlock, a follow-up to the award-winning "30 Rock," in which Burgess had been seen as the flamboyant D'Fwan.
Writers Fey and Carlock will serve as showrunners for the 13-episode comedy, which will star Ellie Kemper.
"Tooken," according to Deadline, "centers on Kimmy (Kemper) who escapes from a doomsday cult and starts life over in New York. Burgess will play a gay, larger-than-life, genuinely talented singer who has never made it to Broadway and lives hand-to-mouth, working as a robot in Times Square. His relationship with Kimmy will re-energize him."