The singer will join actors Hugo Armstrong, Ray Baker and Matthew Carlson, among others, to star in a revival of Martin Sherman's 1979 drama, about a group of gay men trying to survive persecution in Nazi Germany.
Announcing the news of his casting as Greta on Instagram.com, Shears writes, "I'm so happy to be a part of this incredible revival of Bent directed by Moises Kaufman. Previews start July 15th @ the Mark Taper Forum."
Shears will also compose the music for his character's big song, titled Streets of Berlin, which was written by Sherman.
The play had its world premiere in London's West End in 1979, with Sir Ian MCKellen leading the cast as promiscuous gay man Max, while Richard Gere tackled the same role in a 1980 Broadway production.
Sherman also adapted Bent for a film of the same name in 1997, starring Clive Owen.
Shears has previously made minor appearances as an actor in a 2001 short called Versus, and in the independent film The Dramatics: A Comedy, which was released earlier this year (15).
Bent will open on 26 July (15) and run until 23 August (15).