Using Cenozoic and Mesozoic plate motion reconstructions, we derive a model of present-day mantle density heterogeneity under the assumption that subducted slabs sink vertically into the mantle. The thermal buoyancy of these slabs is estimated from the observed thermal subsidence (cooling) of oceanic lithosphere. Slab velocities in the upper mantle are computed from the local convergence rate. We assume that slabs cross the upper/lower mantle interface and continue sinking into the lower mantle with a reduced velocity. For a velocity reduction factor between 2 and 5, our slab heterogeneity model is as correlated with current tomographic models as these models are correlated with each other. We have also computed a synthetic geoid from our density model. For a viscosity increase of about a factor of 40 from the upper to lower mantle, our model predicts the first 8 spherical harmonic degrees of the geoid with statistical confidence larger than 95% and explains 84% of the observed geoid assuming that the model C21 and S21 terms are absent due to a long relaxation time for Earth's rotational bulge. Otherwise, 73% of the geoid variance is explained. The viscosity increase is consistent with our velocity reduction factor for slabs entering the lower mantle, since downwelling velocities are expected to scale roughly as the logarithm of viscosity (log e 40=3.7). These results show that the history of plate tectonics can explain the main features of the present-day structure of the mantle. The dynamic topography induced by this heterogeneity structure consists mainly of about 1-km amplitude lows concentrated along the active continental margins of the Pacific basin. Our model can also be used to predict the time variation of mantle heterogeneity and the gravity field. We find that the ''age'' of the geoid, defined as the time in the past before which the geoid becomes uncorrelated with the present geoid, is about 50 m.y. Our model for the history of the degree 2 geoid, which is equivalent to the history of the inertia tensor, should give us a tool to study the variations in Earth's rotation pole indicated in paleomagnetic studies. ¿ American Geophysical Union 1993