Knowledge of water-surface velocities in rivers is useful for understanding a wide range of lotic processes and systems, such as water and ice fluxes and forces, mixing, solute and sediment transport, bed and bank stability, aquatic and riparian ecology, and extreme hydrologic events. In cold regions, river-ice break up and the associated downstream transport of ice debris is often the most important hydrological event of the year, producing flood levels that commonly exceed those for the open-water period and dramatic consequences for river infrastructure and ecology. Quantification of river surface velocity and currents has relied mostly on very scarce in situ measurements or particle tracking in laboratory models, with few attempts to cover entire river reaches. Accurate and complete surface-velocity fields on rivers have rarely been produced. Here, we use river-ice debris as an index of surface water velocity, and track it over a time period of about one minute, which is the typical time lapse between the two or more images that form a stereo data set in spaceborne, alongtrack optical-stereo mapping. In this way, we measure and visualize for the first time, the almost complete surface velocity field of a river. Examples are used from approximately 80 km and 40 km long reaches of the St. Lawrence and Mackenzie rivers, respectively. The methodology and results will be valuable to a number of disciplines requiring detailed information about river flow, such as hydraulics, hydrology, river ecology and natural-hazard management.