The origin of hotspot trails is controversial. Explanations range from deep mantle plumes rising from the core-mantle boundary (CMB) to shallow plate cracking. However, these mechanisms cannot explain uniquely the scattered hotspot trails distributed across a 2,000-km-wide swell in the sea floor of the southeast Atlantic Ocean. This swell projects down to one of the two largest and deepest distinct regions at the CMB, the Africa Low Shear Wave Velocity Province. Here we use 40 Ar/ 39 Ar isotopic analyses to date lava samples erupted at several hotspot trails across the Atlantic swell. We combine the eruption ages with an analysis of the structure and age of the sea floor, and find that the trails formed synchronously, in a pattern consistent with movement of the African Plate over plumes rising from the edge of the Africa Low Shear Wave Velocity Province. However, we also find that the seamounts initially formed only at the edge of the swell, where the oceanic crust was spreading apart. Later, about 44 million years ago, the hotspot trails began to cross the swell, but only in locations where the lithosphere was sufficiently young and thin that magma could reach the surface. We conclude that the distribution of hotspot trails in the southeast Atlantic Ocean is controlled by the interplay between deep-sourced mantle plumes and the motion and structure of the African Plate.