River networks are striking features engraved into the surface of the Earth, shaped by uplift and erosion under the joint influence of climate and tectonics. How a river’s gradient changes as it descends along its course - its longitudinal profile concavity - varies greatly from one basin to the next, reflecting the interplay between uplift and erosional processes. A recent global analysis has suggested that climatic aridity should be a first-order control on river profile concavity, but the importance of climate relative to other factors has not been tested at global scale. Here, we show, using recent global datasets of climate, river profiles and tectonic activity, that tectonics is much more strongly expressed than climate in global patterns of river profile concavity. River profiles tend to be more strongly concave in tectonically active regions along plate boundaries, reflecting tectonically induced spatial variations in uplift rates. Rank correlations between river profile concavity and four global tectonic proxies (basin-averaged channel gradients, distance to plate boundaries and two measures of seismic activity) are much stronger than those between river concavity and three climate metrics (precipitation, potential evapotranspiration and aridity). We explain the association between tectonic activity and increased river profile concavity through a simple conceptual model of long-term uplift and river incision. These results show that tectonics, and not climate, exerts dominant control on the shape of river longitudinal profiles globally.