The hydraulic permeability and normal stiffness of rock fractures are fundamentally related, which can serve as a probe for assessing hydro-mechanical properties in a variety of geo-engineering contexts. We present experimentally validated numerical simulations of fracture closure and fluid flow processes in realistic aperture structures with mean in the range of 0.01-2 mm. A relatively simple relationship between permeability and normal stiffness is derived in the effective medium regime, using the elastic modulus of the rock matrix, the mean mechanical aperture, and the relative standard deviation (RSD) of the local mechanical aperture. The established relationship between stiffness and permeability appears independent of scale or orientation. Plain Language Summary A natural rock fracture is formed by two rough walls that create complex internal void space structures. Subject to an increasing normal stress, the bridging asperities jointing a fracture deform elastically at first, and then may fail when the local stress reaches critical strength. These elastic and elastic-plastic mechanisms determine the closure behavior of a fracture and the evolution of void spaces that provide the paths for fluid flow. In such a manner, the deformability of a fracture (stiffness) is fundamentally related to the permeability that is controlled by the average aperture of void spaces and their spatial distributions. We prepared a series of natural and synthetic rock fractures with apertures falling in the typical engineering range. By conducting experimental and numerical investigations on the normal loading and fluid flow processes, we were able to obtain a relatively simple relationship between the permeability and normal stiffness in the effective flow regime. This relationship is composed of broadly accepted physical parameters and is independent of scale or direction. It can help the estimation of fracture stiffness from the permeability or fracture permeability from stiffness, depending on which quantity is observable in the field. Key Points Laboratory tests and numerical simulations are combined to analyze the relationship between normal stiffness and permeability in rock fractures Effects of surface roughness, matedness and fracture scale on normal stiffness and permeability are investigated A physically based stiffness-permeability relationship is established for rock fractures in the effective medium regime