She'll take on the title character, portrayed by Mille Dinesen, who found international success on Netflix after winning rave reviews and awards throughout Scandinavia.
The original "Rita" premiered in 2012 and ran for four seasons.
Headey will also executive produce the new Showtime show with creator Christian Torpe, who will write the pilot episode and serve as showrunner.
Headey's villainous Cersei Lannister was killed off in the penultimate episode of "Game of Thrones" and she is reteaming with Nathalie Emmanuel and Natalie Dormer - her former castmates from the show - to voice a role in "The Dark Crystal" prequel series.
The TV reboot of Muppets master Jim Henson's beloved animated puppet franchise will also feature Taron Egerton, Anya Taylor-Joy, Sigourney Weaver, Awkwafina, Helena Bonham Carter, Mark Strong, Alicia Vikander, Mark Hamill, and Jason Isaacs.