Ethiopia is a region where continental rifting gives way to oceanic spreading. Yet the role that pre-existing lithospheric structure, melt, mantle flow, or active upwellings may play in this process is debated. Measurements of seismic anisotropy are often used to attempt to understand the contribution that these mechanisms may play. In this study, we use new data in Afar, Ethiopia along with legacy data across Ethiopia, Djibouti, and Yemen to obtain estimates of mantle anisotropy using SKS-wave splitting. We show that two layers of anisotropy exist, and we directly invert for these. We show that fossil anisotropy with fast directions oriented northeast-southwest may be preserved in the lithosphere away from the rift. Beneath the Main Ethiopian Rift and parts of Afar, anisotropy due to shear segregated melt along sharp changes in lithospheric thickness dominates the shear-wave splitting signal in the mantle. Beneath Afar, away from regions with significant lithospheric topography, melt pockets associated with the crustal and uppermost mantle magma storage dominate the signal in localized regions. In general, little anisotropy is seen in the uppermost mantle beneath Afar suggesting melt retains no preferential alignment. These results show the important role melt plays in weakening the lithosphere and imply that as rifting evolves passive upwelling sustains extension. A dominant northeast-southwest anisotropic fast direction is observed in a deeper layer across all of Ethiopia. This suggests that a conduit like plume is lacking beneath Afar today, rather a broad flow from the southwest dominates flow in the upper mantle.