The ocean floor represents the largest active carbon sink on Earth. However, ocean circulation and the complex shape and topography of the seafloor result in substantial spatial and temporal variations in carbon storage within marine sediments. Here we address this complexity by presenting the first global synthesis of how the depth, shape, and age of the seafloor control the amount of carbon that can potentially be stored in marine sediments. Our results reveal a first-order control by the seafloor relief, with the continental margins and the deep sea accounting for, respectively, ∼59% and ∼40% of the global seafloor carbon storage. These environments show contrasting controls, with the continental margins influenced by the seafloor shape (i.e., slope) and the deep sea by seafloor roughness and water depth. Our findings provide important constraints for predicting how the ocean carbon sink could evolve in response to the anticipated expansion of oxygen minimum zones and ocean acidification under global change scenarios.