The Fermi Gamma-Ray Space Telescope reveals a diffuse inverse Compton signal in the inner Galaxy with the same spatial morphology as the microwave haze observed by WMAP, confirming the synchrotron origin of the microwaves. Using spatial templates, we regress out pi0 gammas, as well as ICS and bremsstrahlung components associated with known soft-synchrotron counterparts. We find a significant gamma-ray excess towards the Galactic center with a spectrum that is significantly harder than other sky components and is most consistent with ICS from a hard population of electrons. The morphology and spectrum are consistent with it being the ICS counterpart to the electrons which generate the microwave haze seen at WMAP frequencies. In addition to confirming that the microwave haze is indeed synchrotron, the distinct spatial morphology and very hard spectrum of the ICS are evidence that the electrons responsible for the microwave and gamma-ray haze originate from a harder source than supernova shocks. We describe the full sky Fermi maps used in this analysis and make them available for download.