Recent advances in metasurfaces have shown the importance of controlling the bianisotropic response of the constituent meta-atoms for maximum efficiency wave-front transformation. By carefully designing the bianisotropic response of the metasurface, full control of the local transmission and reflection properties is enabled, opening new design avenues for creating reciprocal metasurfaces. Despite recent advances in the highly efficient transformation of both electromagnetic and acoustic plane waves, the importance of bianisotropic metasurfaces for transforming cylindrical waves is still unexplored. Motivated by the possibility of arbitrarily controlling the angular momentum of cylindrical waves, we develop a design methodology of a bianisotropic cylindrical metasurface that enables transformation of cylindrical waves for both acoustic and electromagnetic waves with theoretically 100% power efficiency. This formalism is further validated in the acoustic scenario where an experimental demonstration of highly efficient angular momentum transformation is shown.