We propose a new kinematic framework for the East African rift system linking the development of the Eastern and Western rifts via stress transmission across the Archean Tanzania craton. The proposal is based on three observations. (1) A new map of uppermost-mantle P-wave velocities beneath Tanzania, in combination with the results of other seismic, gravity, heat-flow, and xenolith studies, reveals that the craton's thick, cold lithosphere has largely resisted modification by the Cenozoic extensional tectonism and has therefore behaved as a rigid tectonic block. (2) As the southward-propagating Eastern rift reached the craton margin ca. 12–10 Ma, the Western rift began to develop. (3) Subsequently, the Western rift enlarged into a 2500-km-long system of en echelon rift basins while development of the Eastern rift stalled where it ran into the craton. These observations suggest that when the Eastern rift reached the margin of the rigid craton ca. 12–10 Ma, the transmission of extensional stresses across the strong cratonic lithosphere caused rift faulting to develop in the weaker mobile-belt lithosphere on the west side of the craton. This new kinematic framework for rift development is consistent with models for both active and passive rifting in East Africa.