Embedded germanium nanocrystals (NCs) in a silica host matrix are theoretically analyzed to identify their third-order bound-state nonlinearities. A rigorous atomistic pseudopotential approach is used for determining the electronic structure and the nonlinear optical susceptibilities. This study characterizing the two-photon absorption, nonlinear refractive index, and optical switching parameters reveals the full wavelength dependence from static up to the ultraviolet spectrum, and the size dependence up to a diameter of 3.5 nm. Similar to Si NCs, the intensity-dependent refractive index increases with decreasing NC diameter. On the other hand, Ge NCs possess about an order of magnitude smaller nonlinear susceptibility compared to Si NCs of the same size. It is observed that the two-photon absorption threshold extends beyond the half band-gap value. This enables nonlinear refractive index tunability over a much wider wavelength range free from two-photon absorption.