ArcticDEM is a collection of 2‐m resolution, repeat digital surface models created from stereoscopic satellite imagery. To demonstrate the potential of ArcticDEM for measuring river stages and discharges, we estimate river surface heights along a reach of Tanana River near Fairbanks, Alaska, by the precise detection of river shorelines and mapping of shorelines to land surface elevation. The river height profiles over a 15‐km reach agree with in situ measurements to a standard deviation less than 30 cm. The time series of ArcticDEM‐derived river heights agree with the U.S. Geological Survey gage measurements with a standard deviation of 32 cm. Using the rating curve for that gage, we obtain discharges with a validation accuracy (root‐mean‐square error) of 234 m3/s (23% of the mean discharge). Our results demonstrate that ArcticDEM can accurately measure spatial and temporal variations of river surfaces, providing a new and powerful data set for hydrologic analysis.