The concavity, or curvature, of river profiles has long been taken to be a fundamental indicator of the underlying processes governing fluvial erosion, and thereby of landscape evolution. However, erosion laws have generally been derived without accounting for the strong orographically driven gradients in precipitation typically found in mountainous regions. In addition, field measurements have found discrepancies between the form of measured stream profiles and theoretically derived values. Introducing a simple physically based feedback, we find that orographically induced variations in precipitation strongly affect the curvature of steady-state river profiles. This feedback complicates efforts to infer the form of erosion laws from observed profile concavities, but could help explain discrepancies between observations and theory. Our results demonstrate a strong feedback through which climate influences the form of river profiles and show how such climatic effects act to limit the relief of unglaciated mountain ranges.