Variations in rock strength act as a first‐order control on mountain landscapes. However, the transient topographic signal of basement exhumation has not been explored. We use model outputs to demonstrate the mobility of drainage divides in mountain ranges in response to the exhumation of basement rocks and the implications for the morphology of river catchments. The exhumation of harder rocks within a catchment reduces upstream channel steepness and erosion rates in contrast to neighbouring catchments. The results are a shift in the orogen‐scale drainage divide towards the harder rocks, and the formation of range parallel longitudinal valleys as neighbouring river networks capture the headwaters of catchments impacted by the harder lithology. Our model outputs provide a process explanation for the initiation of many longitudinal valleys in mountain ranges, and for the pinning of drainage divides on rocks of higher strength as seen the Central Pyrenees, Western Alps or High Atlas.