We demonstrate efficient Förster resonance energy transfer (FRET) from a thin film of phosphorescent dye, fac tris(2-phenylpyridine) iridium (Ir(ppy)3), to a thin film of J-aggregated cyanine dye, 5,6-dichloro-2-[3-[5,6-dichloro-1-ethyl-3-(3-sulfopropyl)-2(3H)-benzimidazolidene]-1-propenyl]-1-ethyl-3-(3-sulfopropyl) benzimidazolium hydroxide (TDBC). The measurement is performed on a planar sandwich structure with the layer of Ir(ppy)3 and the layer of J-aggregates separated by a uniform optically inert spacer layer. Quenching of Ir(ppy)3 photoluminescence due to FRET of Ir(ppy)3 excitons to J-aggregates enables us to calculate the experimentally-determined Förster radius of 3.8 nm, which is in good agreement with the theoretically calculated value.