After a large subduction earthquake, crustal deformation continues to occur, with a complex pattern of evolution. This postseismic deformation is due primarily to viscoelastic relaxation of stresses induced by the earthquake rupture and continuing slip (afterslip) or relocking of different parts of the fault. When postseismic geodetic observations are used to study Earth's rheology and fault behaviour, it is commonly assumed that short-term (a few years) deformation near the rupture zone is caused mainly by afterslip, and that viscoelasticity is important only for longer-term deformation. However, it is difficult to test the validity of this assumption against conventional geodetic data. Here we show that new seafloor GPS (Global Positioning System) observations immediately after the great Tohoku-oki earthquake provide unambiguous evidence for the dominant role of viscoelastic relaxation in short-term postseismic deformation. These data reveal fast landward motion of the trench area, opposing the seaward motion of GPS sites on land. Using numerical models of transient viscoelastic mantle rheology, we demonstrate that the landward motion is a consequence of relaxation of stresses induced by the asymmetric rupture of the thrust earthquake, a process previously unknown because of the lack of near-field observations. Our findings indicate that previous models assuming an elastic Earth will have substantially overestimated afterslip downdip of the rupture zone, and underestimated afterslip updip of the rupture zone; our knowledge of fault friction based on these estimates therefore needs to be revised.