Identifying the causes of historical trends in relative sea level-the height of the sea surface relative to Earth's crust-is a prerequisite for predicting future changes. Rates of change along the eastern coast of the USA (the US East Coast) during the past century were spatially variable, and relative sea level rose faster along the Mid-Atlantic Bight than along the South Atlantic Bight and the Gulf of Maine. Past studies suggest that Earth's ongoing response to the last deglaciation(1-5), surface redistribution of ice and water(5-9) and changes in ocean circulation(9-13) contributed considerably to this large-scale spatial pattern. Here we analyse instrumental data(14,15) and proxy reconstructions(4,12) using probabilistic methods(16-18) to show that vertical motions of Earth's crust exerted the dominant control on regional spatial differences in relative sea-level trends along the US East Coast during 1900-2017, explaining most of the large-scale spatial variance. Rates of coastal subsidence caused by ongoing relaxation of the peripheral forebulge associated with the last deglaciation are strongest near North Carolina, Maryland and Virginia. Such structure indicates that Earth's elastic lithosphere is thicker than has been assumed in other models(19-22). We also find a substantial coastal gradient in relative sea-level trends over this period that is unrelated to deglaciation and suggests contributions from twentieth-century redistribution of ice and water. Our results indicate that the majority of large-scale spatial variation in long-term rates of relative sea-level rise on the US East Coast is due to geological processes that will persist at similar rates for centuries.