Glenn, who plays Brook Soso in the award-winning Netflix series, will co-star in the musical adaptation of the 2007 film Waitress with songs by pop star Sara Bareilles.
Waitress, which starred Keri Russell in the film, tells the story of a waitress and pie maker trapped in a loveless marriage. Glenn joins a cast that includes Jessie Mueller, Eric Anderson and Christopher Fitzgerald.
Glenn, who has a recurring role on FX's Married, will join on Broadway this season actress Danielle Brooks, who plays Taystee on Orange Is the New Black and will star as Sofia in a revival of The Colour Purple.
Orange actress Uzo Aduba is also in The Wiz Live!