Unsustainable rates of groundwater (GW) depletion make GW management a priority. Effective GW management is hindered by the uncertainty in the predictions of aquifer models, but the increase of geodetic surface deformation data can improve aquifer characterization. We integrate surface deformation measurements into a Bayesian inference framework to infer aquifer permeability in a poroelastic model. We demonstrate the applicability of this technique using a Nevada pumping test with both Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) surface deformation data. We infer the lateral permeability variations in the aquifer with high spatial resolution and identify the information content of each data set. For the Nevada case, a single InSAR surface deformation map provides significantly more information than multiple GPS time series. As the availability of global InSAR data continues to grow, geomechanical inversion of geodetic surface deformation data will become a valuable technique for aquifer characterization and management.