We develop three-dimensional finite element models incorporating a subducting India slab to investigate the dynamic mechanisms of postseismic deformation processes following the 2015 Mw 7.8 Gorkha earthquake based on nearly 5 years of GPS data in Nepal and southern Tibet. At first, we explore two simple models that consider viscoelastic relaxation and stress-driven afterslip as the individual mechanism, but find that single mechanism cannot fully explain the observations holistically. Therefore, we present a combined model that simultaneously resolves the trade-off of individual contributions from viscoelastic relaxation and afterslip by evaluating the misfit between the simulated and observed time series. The combined model reproduces the postseismic deformation associated with the Gorkha earthquake and indicates that near- to intermediate-field postseismic displacements are mainly caused by aseismic slip on the downdip of the coseismic rupture, while the far-field deformation is dominated by viscoelastic relaxation in the lower crust and upper mantle of the southern Tibet. The steady-state viscosity of the lower crust in the southern Tibet is estimated to be $3\times {10}^{18}Pas$, corresponding transient-state viscosity is $3\times {10}^{17}Pas$. The best combined model suggests that approximately 90% afterslip was released in the first 4 years and corresponding frictional parameter $a\sigma =0.15\mathrm{M}\mathrm{P}\mathrm{a}$. Also, we find the afterslip fringing the downdip of the coseismic rupture plays an important role in the trade-off between near- and intermediate-field displacements. Afterslip deficit in the shallow part of the Main Himalayan Thrust indicates the potential seismic hazard on the south and west of Kathmandu in future.