Crustal structure in Kenya and Ethiopia has been investigated using receiver function analysis of broadband seismic data to determine the extent to which the Cenozoic rifting and magmatism has modified the thickness and composition of the Proterozoic crust in which the East African rift system developed. Data for this study come from broadband seismic experiments conducted in Ethiopia between 2000 and 2002 and in Kenya between 2001 and 2002. Two methods have been used to analyze the receiver functions, the H-$kappa$ method, and direct stacks of the waveforms, yielding consistent results. Crustal thickness to the east of the Kenya rift varies between 39 and 42 km, and Poisson's ratios for the crust vary between 0.24 and 0.27. To the west of the Kenya rift, Moho depths vary between 37 and 38 km, and Poisson's ratios vary between 0.24 and 0.27. These findings support previous studies showing that crust away from the Kenya rift has not been modified extensively by Cenozoic rifting and magmatism. Beneath the Ethiopian Plateau on either side of the Main Ethiopian Rift, crustal thickness ranges from 33 to 44 km, and Poisson's ratios vary from 0.23 to 0.28. Within the Main Ethiopian Rift, Moho depths vary from 27 to 38 km, and Poisson's ratios range from 0.27 to 0.35. A crustal thickness of 25 km and a Poisson's ratio of 0.36 were obtained for a single station in the Afar Depression. These results indicate that the crust beneath the Ethiopian Plateau has not been modified significantly by the Cenozoic rifting and magmatism, even though up to a few kilometers of flood basalts have been added, and that the crust beneath the rifted regions in Ethiopia has been thinned in many places and extensively modified by the addition of mafic rock. The latter finding is consistent with models for rift evolution, suggesting that magmatic segments with the Main Ethiopian Rift, characterized by dike intrusion and Quaternary volcanism, act now as the locus of extension rather than the rift border faults.