In this study, we propose a low-cost, simple and feasible post-processing approach to improve the light extraction efficiency (LEE) of LED packages. Amorphous photonic structures (APSs) with only short-range order are fabricated from anodic aluminum oxide (AAO) and transferred to intermediate polymer stamp (IPS) by nanoimprint technology. The IPS with APSs is directly mounted onto the surface of an LED package, where the LEE is achieved as 94.6%. The scanning electron microscope (SEM) images of AAO templates and imprinted IPS are analyzed by radial distribution function and diameter histogram. The far-field patterns of APS-mounted LED packages are measured in electroluminescence (EL). The three-dimensional finite-difference time-domain (3D-FDTD) calculations of transmittance of APSs confirm that they improve the light extraction above the critical angle. Two-dimensional Fourier power spectra from SEM images of APSs are also calculated. The LEE enhancement is attributed to that the APSs have short-range order on a length scale comparable to emission wavelength of LED. We provide novel multistage simulations in a simplified FDTD model for the LED package. Finally, we discuss the influence of the morphology of APSs on the LEE of the APS mounted LEDs.