East Africa is a tectonically complex region owing to the presence of a rigid craton, paleothrust belts and shear zones, active magmatism and rifting, and possibly even a mantle plume. We present new splitting results of teleseismic shear phases recorded by 21 broadband seismic stations in Tanzania, seven broadband stations in Kenya, and three permanent broadband Global Seismic Network stations in Kenya and Uganda. Inconsistent apparent splitting is observed beneath the craton and along its southern and southeastern flank in Tanzania. Splitting at stations elsewhere in the rifts and orogenic belts is more consistent. We test between different models of anisotropy for stations with inconsistent splitting (single layer with horizontal fast axis, single layer with dipping fast axis, and two layers with horizontal fast axes). However, we show that these more complicated models do not reasonably explain the data. The data are explained better by a laterally (and/or in some places vertically) varying single-layer model with a horizontal fast axis. We arrive at a conceptual model of anisotropy in Tanzania and Kenya that is controlled by (1) active shear along the base of the plate associated with asthenospheric flow beneath and around the moving craton keel, (2) asthenospheric flow from a plume north of central Kenya, (3) fossilized anisotropy in the lithosphere due to past orogenic events, and possibly (4) aligned magma-filled lenses beneath the rifts. Our most robust conclusion is that we can rule out an extension-induced lattice preferred orientation of olivine as a dominant factor, which is surprising given the long history of extension in the region. This indicates that mantle-lithospheric extension in East Africa occurs via dike intrusion and/or ductile thinning within narrow rift zones and is possibly facilitated by a mechanical lithospheric anisotropy imparted by fossilized north/south structural or mineralogical fabrics.