©2017. American Geophysical Union. All Rights Reserved. We analyze three-dimensional GPS coordinate time series from continuously operating stations in Nepal and South Tibet and calculate the initial 1 year postseismic displacements. We first investigate models of poroelastic rebound, afterslip, and viscoelastic relaxation individually and then attempt to resolve the trade-offs between their contributions by evaluating the misfit between observed and simulated displacements. We compare kinematic inversions for distributed afterslip with stress-driven afterslip models. The modeling results show that no single mechanism satisfactorily explains near- and far-field postseismic deformation following the Gorkha earthquake. When considering contributions from all three mechanisms, we favor a combination of viscoelastic relaxation and afterslip alone, as poroelastic rebound always worsens the misfit. The combined model does not improve the data misfit significantly, but the inverted afterslip distribution is more physically plausible. The inverted afterslip favors slip within the brittle-ductile transition zone downdip of the coseismic rupture and fills the small gap between the mainshock and largest aftershock slip zone, releasing only 7% of the coseismic moment. Our preferred model also illuminates the laterally heterogeneous rheological structure between India and the South Tibet. The transient and steady state viscosities of the upper mantle beneath Tibet are constrained to be greater than 1018 Pa s and 1019 Pa s, whereas the Indian upper mantle has a high viscosity ≥1020 Pa s. The viscosity in the lower crust of southern Tibet shows a clear trade-off with its southward extent and thickness, suggesting an upper bound value of ~8 × 1019 Pa s for its steady state viscosity.