Climate proxy data and numerical models suggest that latitudinal displacements of the Intertropical Convergence Zone (ITCZ) occur during millennial-scale cold events in the North Atlantic region, but the potential effects of these ITCZ movements on the climate of equatorial regions are unclear. Here we present a 5400-year geochemical record of rainfall and drought from Lake Edward in equatorial Africa. We observe a non-linear correlation in which drought in equatorial Africa occurs during both cold and warm extremes in the North Atlantic's 1500-year quasi-cycle. We propose that this relationship occurs due to northward/southward displacement of the ITCZ from its equatorial mean position during warm/cold events. Our results show that millennial-scale high-latitude climate events are linked to changes in equatorial terrestrial climate even during the late Holocene and suggest important constraints on the mechanisms linking tropical and extratropical climate variability.