Continental rift systems form by propagation of isolated rift segments that interact, and eventually evolve into continuous zones of deformation. This process impacts many aspects of rifting including rift morphology at breakup, and eventual ocean-ridge segmentation. Yet, rift segment growth and interaction remain enigmatic. Here we present geological data from the poorly documented Ririba rift (South Ethiopia) that reveals how two major sectors of the East African rift, the Kenyan and Ethiopian rifts, interact. We show that the Ririba rift formed from the southward propagation of the Ethiopian rift during the Pliocene but this propagation was short-lived and aborted close to the Pliocene-Pleistocene boundary. Seismicity data support the abandonment of laterally offset, overlapping tips of the Ethiopian and Kenyan rifts. Integration with new numerical models indicates that rift abandonment resulted from progressive focusing of the tectonic and magmatic activity into an oblique, throughgoing rift zone of near pure extension directly connecting the rift sectors.