The rate of river migration affects the stability of Arctic infrastructure and communities1,2 and regulates the fluxes of carbon3,4, nutrients5 and sediment6,7 to the oceans. However, predicting how the pace of river migration will change in a warming Arctic8 has so far been stymied by conflicting observations about whether permafrost9 primarily acts to slow10,11 or accelerate12,13 river migration. Here we develop new computational methods that enable the detection of riverbank erosion at length scales 5-10times smaller than the pixel size in satellite imagery, an innovation that unlocks the ability to quantify erosion at the sub-monthly timescales when rivers undergo their largest variations in water temperature and flow. We use these high-frequency observations to constrain the extent to which erosion is limited by the thermal condition of melting the pore ice that cements bank sediment14, a requirement that will disappear when permafrost thaws, versus the mechanical condition of having sufficient flow to transport the sediment comprising the riverbanks, a condition experienced by all rivers15. Analysis of high-resolution data from the Koyukuk River, Alaska, shows that the presence of permafrost reduces erosion rates by 47%. Using our observations, we calibrate and validate a numerical model that can be applied to diverse Arctic rivers. The model predicts that full permafrost thaw may lead to a 30-100% increase in the migration rates of Arctic rivers.