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SUMMARY Geodetic observations of post-seismic deformation due to afterslip and viscoelastic relaxation can be used to infer fault and lithosphere rheologies by combining the observations with mechanical models of post-seismic processes. However, estimating the spatial distributions of rheological parameters remains challenging because it requires solving a nonlinear inverse problem with a high-dimensional parameter space and potentially computationally expensive forward model. Here we introduce an inversion method to estimate spatially varying fault and lithospheric rheological parameters in a mechanical model of post-seismic deformation using geodetic time series. The forward model combines afterslip and viscoelastic relaxation governed by a velocity-strengthening frictional rheology and a power-law Burgers rheology, respectively, and incorporates the mechanical coupling between coseismic slip, afterslip and viscoelastic relaxation. The inversion method estimates spatially varying fault frictional parameters, viscoelastic constitutive parameters and coseismic stress change. We formulate the inverse problem in a Bayesian framework to quantify the uncertainties of the estimated parameters. To solve this problem with reasonable computational costs, we develop an algorithm to estimate the mean and covariance matrix of the posterior probability distribution based on an ensemble Kalman filter. We validate our method through numerical tests using a 2-D forward model and synthetic post-seismic GNSS time-series. The test results suggest that our method can estimate the spatially varying rheological parameters and their uncertainties reasonably well with tolerable computational costs. Our method can also recover spatially and temporally varying afterslip, viscous strain and effective viscosities and can distinguish the contributions of afterslip and viscoelastic relaxation to observed post-seismic deformation.