River networks are striking features engraved into Earth's surface, shaped by uplift and erosion under the joint influence of climate and tectonics. How a river descends along its course -its longitudinal profile -varies greatly from one basin to the next, reflecting the interplay between uplift and erosional processes. It has recently been argued that climatic aridity should be a firstorder 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 river profiles and tectonic activity, that tectonics is much more strongly expressed than climate in global patterns in 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 global tectonic proxies (basin slope and two indices of seismic risk) are much stronger than those between river concavity and precipitation, potential evapotranspiration, or aridity. These results show that tectonics, and not climate, exerts first-order control on the shape of river longitudinal profiles globally.