Mantle viscosity controls a variety of geodynamic processes, e.g. Glacial Isostatic Adjustment (GIA). Constraining GIA using better viscosity estimates would improve our estimates of recent ice mass loss from the Greenland and Antarctic ice sheets and the associated sea level rise. However, mantle viscosity is poorly constrained as it can rarely be measured directly, making geophysical observations that could place constraints on viscosity more essential. Empirically, viscosity is mainly controlled by temperature, water content of nominally anhydrous minerals, partial melt, grain size and stress. Of these, temperature, water content, and the presence of partial melt can be inferred from seismic and magnetotelluric (MT) measurements, which are important tools in imaging the subsurface of the Earth. In this study, we develop a method to estimate mantle viscosity in which we: (1) constrain temperature from MT, seismic, and surface heat flow observations; (2) constrain compositional structure (i.e., water content and partial melt) from MT and seismic data coupled with experimental mineral physics data; and finally, (3) convert the calculated thermal and compositional structures into a viscosity structure. In each step, we assess and quantify the involved uncertainties. In addition, we introduce a useful parameter – the viscosity ratio (a ratio between viscosities of a target region and a nearby reference region at the same stress and grain size), and quantify its amplitude and uncertainty for a range of temperatures and water contents. We find that the uncertainty in this ratio is relatively small when computed from both seismic and MT observations, compared to either constraint applied alone. We also explore how viscosity ratio uncertainties vary with grain size and stress. Information about grain size can potentially be obtained from seismic attenuation or tectonic history. Overall, we find that both seismic and MT observations can considerably improve estimates of mantle viscosity, and place useful constraints on its lateral variations in the upper mantle. Geophysically-derived mantle viscosity models can be calibrated in areas like Scandinavia, which has well-constrained GIA models, and applied to polar regions where the GIA response is poorly known.