Earth’s mantle composition is essential to our understanding of its physics and dynamics. Here we report single-crystal elasticity (Cij) of (Al,Fe)-bearing bridgmanite, Mg0.88Fe0.1Al0.14Si0.90O3 with Fe3+/∑Fe=~0.65, up to ~82 GPa measured in diamond anvil cells. Together with heat capacity measurements on bridgmanite and ferropericlase, we develop a fully internally-consistent thermoelastic model to simultaneously evaluate lower-mantle mineralogy and geotherm via comparisons of P-wave, S-wave velocities, and density (VP, VS, and ρ) with one-dimensional seismic profiles. Our best-fit model demonstrates the lower mantle consists of ~89 vol% (Al,Fe)-bearing bridgmanite, ~4 vol% ferropericlase, and ~7 vol% CaSiO3 perovskite. A chemically layered mantle with pyrolitic upper mantle and bridgmanite-predominant lower mantle would display ~3.2(±1.5)%, ~5.2(±1.5)%, and ~5.0(±1.0)% jumps in VP, VS, and ρ, respectively, across the 660-km discontinuity, which are well consistent with seismic reflection observations. The lower mantle could have become bridgmanite-predominant via accumulations of ancient silica-rich materials, which helps explain current deep-Earth seismic and geochemical signatures.