On the Beagle voyage, Charles Darwin first noted the creation and subsidence of ocean islands¹, establishing in geology’s infancy that island freeboard changes with time. Hotspot ocean islands have an obvious mechanism for freeboard change through the growth of the bathymetric anomaly, or swell², on which the islands rest. Models for swell development indicate that flexural⁹, thermal^2,3 or dynamic pressure^4,5,6,8 contributions, as well as spreading of melt residue from the hotspot⁷, can all contribute to island uplift. Here we test various models for swell development using the uplift histories for the islands of the Cape Verde hotspot, derived from isotopic dating of marine terraces and subaerial to submarine lava-flow morphologies. The island uplift histories, in conjunction with inter-island spacing, uplift rate and timing differences, rule out flexural, thermal or dynamic pressure contributions. We also find that uplift cannot be reconciled with models that advocate the spreading of melt residue in swell development unless swell growth is episodic. Instead, we infer from the uplift histories that two processes have acted to raise the islands during the past 6 Myr. During an initial phase, mantle processes acted to build the swell. Subsequently, magmatic intrusions at the island edifice caused 350 m of local uplift at the scale of individual islands. Finally, swell-wide uplift contributed a further 100 m of surface rise.