The western branch of the East African Rift is composed of an arcuate succession of elongate asymmetric basins, which differ in terms of interaction geometry, fault architecture and kinematics, and patterns of uplift/subsidence and erosion/sedimentation. The basins are located within Proterozoic mobile belts at the edge of the strong Tanzanian craton; surface geology suggests that the geometry of these weak zones is an important parameter in controlling rift development and architecture, although other processes have been proposed. In this study, we use lithosphere‐scale numerical models and crustal‐scale analogue experiments to shed light on the relations between preexisting structures and rift architecture. Results illustrate that on a regional scale, rift localization within the mobile belts at the curved craton's western border results in an arcuate rift system, which implies that under a constant extensional stress field, part of the western branch experienced orthogonal extension and part oblique extension. Largest depocenters are predicted to form mostly orthogonal to the extension direction, and smaller depocenters will form along the oblique parts of the rift. The varying extension direction along the rift zone furthermore results in lengthwise varying rift asymmetry, segmentation characteristics, and border fault architecture (trend, length, and kinematics). Analogue models predict that discrete upper crustal fabrics may influence the location of accommodation zones and control the architecture of extension‐related faults at a local scale. Models support that fabric reactivation is responsible for the oblique‐slip kinematics on faults and for the development of Z‐shaped or arcuate normal faults typically documented in nature.