Large tectonic earthquakes lead to significant deformations in the months and years thereafter. These so-called post-seismic deformations include contributions mainly from afterslip and viscoelastic relaxation, quantification of their relative influence is of importance for understanding the evolution of post-seismic crustal stress, strain and aftershocks. Here, we investigate the post-seismic deformation processes following the 2011 Mw 9.0 Tohoku earthquake using surface displacement data as observed by the onshore global positioning system network in the first ∼1.5 yr following the main shock. We explore two different inversion modelling strategies: (i) we simulate pure afterslip and (ii) we simulate the combined effect of afterslip and viscoelastic relaxation. By assuming that the afterslip is solely responsible for the observed post-seismic deformation, we find most afterslip activities to be located close to the downdip area of the coseismic rupture at 20–80 km depth with a maximum cumulative slip of ∼3.8 m and a seismic moment of 2.3 × 1022 Nm, equivalent in moment to an Mw 8.84 earthquake. By assuming a combination of afterslip and viscoelastic components, the best data fit is found for an afterslip portion that is spatially consistent with the pure afterslip model, but reveals a decreased seismic moment of 2.1 × 1022 Nm, or Mw 8.82. In addition, the combined model suggests an effective thickness of the elastic crust of ∼50 km overlying an asthenosphere with a Maxwell viscosity of 2 × 1019 Pa s. Temporal analysis of our model inversions suggests that the rate of afterslip rapidly decreases with time, consistent with the state- and rate-strengthening frictional law. The spatial pattern of afterslip coincides with the locations of aftershocks, and also with the area of coseismically increased Coulomb failure stress (CFS). Only a small part of the coseismically increased CFS was released by the afterslip in 564 d after the event. The effect of the viscoelastic relaxation within this initial stage only plays a secondary role, but it shows an increasing tendency, that is, the contribution of viscoelastic relaxation increases with time. Further geodetic observations are needed for a robust quantification of the role of the viscoelastic relaxation in the post-seismic deformation.