The East African rift in Ethiopia is unique worldwide because it captures the final stages of transition from continental rifting to seafloor spreading. A recent study there has shown that magma intrusion plays an important role during the final stages of continental breakup, but the mechanism by which it is incorporated into the extending plate remains ambiguous: wide-angle seismic data and complementary geophysical tools such as gravity analysis are not strongly sensitive to the geometry of subsurface melt intrusions. Studies of shear wave splitting in near-vertical SKS phases beneath the transitional Main Ethiopian Rift (MER) provide strong and consistent evidence for a rift-parallel fast anisotropic direction. However, it is difficult to discriminate between oriented melt pocket (OMP) and lattice preferred orientation (LPO) causes of anisotropy based on SKS study alone. The speeds of horizontally propagating Love (SH) and Rayleigh (SV) waves vary in similar fashions with azimuth for LPO- and OMP-induced anisotropy, but their relative change is distinctive for each mechanism. This diagnostic is exploited by studying the propagation of surface waves from a suite of azimuths across the MER. Anisotropy is roughly perpendicular to the absolute plate motion direction, thus ruling out anisotropy due to the slowly moving African Plate. Instead, three mechanisms for anisotropy act beneath the MER: periodic thin layering of seismically fast and slow material in the uppermost ∼10 km, OMP between ∼20–75 km depth, and olivine LPO in the upper mantle beneath. The results are explained best by a model in which low aspect ratio melt inclusions (dykes and veins) are being intruded into an extending plate during late stage breakup. The observations from Ethiopia join a growing body of evidence from rifts and passive margins worldwide that shows magma intrusion plays an important role in accommodating extension without marked crustal thinning.