Constraining the chemical, rheological and electromagnetic properties of the lowermost mantle (D'') is important to understand the formation and dynamics of the Earth's mantle and core. To explain the origin of the variety of characteristics of this layer observed with seismology, a number of theories have been proposed, including core-mantle interaction, the presence of remnants of subducted material and that D'' is the site of a mineral phase transformation. This final possibility has been rejuvenated by recent evidence for a phase change in MgSiO3 perovskite (thought to be the most prevalent phase in the lower mantle) at near core-mantle boundary temperature and pressure conditions. Here we explore the efficacy of this 'post-perovskite' phase to explain the seismic properties of the lowermost mantle through coupled ab initio and seismic modelling of perovskite and post-perovskite polymorphs of MgSiO3, performed at lowermost-mantle temperatures and pressures. We show that a post-perovskite model can explain the topography and location of the D'' discontinuity, apparent differences in compressional- and shear-wave models and the observation of a deeper, weaker discontinuity. Furthermore, our calculations show that the regional variations in lower-mantle shear-wave anisotropy are consistent with the proposed phase change in MgSiO3 perovskite.