© 2015 Elsevier B.V.. Consideration of the three-dimensional heterogeneity of mantle rheology allows models of viscoelastic relaxation following the 2004 Sumatra-Andaman earthquake to simultaneously fit both the observed far-field and near-field postseismic deformation. We use horizontal and vertical campaign and continuous GPS observations from the Andaman, Nicobar, and Sumatran forearc islands, mainland Sumatra, Thailand, the Malay Peninsula, the Indian Ocean, and southern India, spanning the first five years of postseismic deformation. The postseismic relaxation models consider contributions from the 2004 Mw 9.2 Sumatra-Andaman, the 2005 Mw 8.7 Nias, and 2007 Mw 8.4 Bengkulu earthquakes. Far-field motions to the east of the ruptures are equally well fit by homogeneous or laterally variable earth models. However, only models with contrasting rheology across the subducting slab, a ten-times higher mantle viscosity under the Indian Ocean lithosphere than the backarc mantle, can also produce the observed enduring postseismic uplift along the forearc and lack of far-field transient displacements in southern India. While postseismic uplift of forearc stations can also be produced by rapid and enduring down-dip afterslip, the inferred rheology structure is consistent with the distribution of mantle temperature inferred from seismic tomography.