River drainage patterns sculpt terrestrial landscapes. Whether these patterns contain fingerprints of past tectonic events is debated. On the one hand, elaborate dendritic river networks always retain an invariant structure, implying that rivers will simply reorganize in response to tectonic perturbations, without long-term trace of the tectonic event. On the other hand, many rivers in active mountain belts seem to be passive features and may record long-term crustal deformation. Here we use numerical simulations, constrained by drainage patterns observed in the Southern Alps of New Zealand, to analyse the response of river basins to distributed plate tectonic strain.We find that both dynamically reorganized and passively deformed rivers coexist in the Southern Alps. Rivers on the western side of the mountain range reorganize and rapidly evolve in response to tectonic deformation. In contrast, rivers on the eastern side resist reorganization and record large-scale plate tectonic influence over timescales of tens of millions of years.We conclude that both types of river drainage pattern in the Southern Alps are primarily controlled by plate tectonic strain, implying that landscape topography can be used to reconstruct the distribution of tectonic strain within zones of continental deformation around the world.