A key scientific and technological challenge in organic light-emitting diodes (OLEDs) is enhancing the light outcoupling factor ηout, which is typically <20%. This paper reports experimental and modeling results of a promising approach to strongly increase ηout by fabricating OLEDs on novel flexible nanopatterned substrates that result in a >2× enhancement in green phosphorescent OLEDs (PhOLEDs) fabricated on corrugated polycarbonate (PC). The external quantum efficiency (EQE) reaches 50% (meaning ηout ≥50%); it increases 2.6x relative to a glass/ITO device and 2× relative to devices on glass/poly(3,4-ethylenedioxythiophene):polystyrene sulfonate (PEDOT:PSS) or flat PC/PEDOT:PSS. A significant enhancement is also observed for blue PhOLEDs with EQE 1.7× relative to flat PC. The corrugated PC substrates are fabricated efficiently and cost-effectively by direct room-temperature molding. These substrates successfully reduce photon losses due to trapping/waveguiding in the organic+anode layers and possibly substrate, and losses to plasmons at the metal cathode. Focused ion beam gauged the conformality of the OLEDs. Dome-shaped convex nanopatterns with height of ∼280–400 nm and pitch ∼750–800 nm were found to be optimal. Substrate design and layer thickness simulations, reported first for patterned devices, agree with the experimental results that present a promising method to mitigate photon loss paths in OLEDs.