Epitaxially oriented wafer-scale graphene grown directly on semiconducting Ge substrates is of high interest for both fundamental science and electronic device applications. To date, however, this material system remains relatively unexplored structurally and electronically, particularly at the atomic scale. To further understand the nature of the interface between graphene and Ge, we utilize ultrahigh vacuum scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) along with Raman and X-ray photoelectron spectroscopy to probe interfacial atomic structure and chemistry. STS reveals significant differences in electronic interactions between graphene and Ge(110)/Ge(111), which is consistent with a model of stronger interaction on Ge(110) leading to epitaxial growth. Raman spectra indicate that the graphene is considerably strained after growth, with more point-to-point variation on Ge(111). Furthermore, this native strain influences the atomic structure of the interface by inducing metastable and previously unobserved Ge surface reconstructions following annealing. These nonequilibrium reconstructions cover >90% of the surface and, in turn, modify both the electronic and mechanical properties of the graphene overlayer. Finally, graphene on Ge(001) represents the extreme strain case, where graphene drives the reorganization of the Ge surface into [107] facets. From this work, it is clear that the interaction between graphene and the underlying Ge is not only dependent on the substrate crystallographic orientation, but is also tunable and strongly related to the atomic reconfiguration of the graphene-Ge interface.