Skilful climate predictions of the winter North Atlantic Oscillation and Arctic Oscillation out to a few months ahead have recently been demonstrated, but the source of this predictability remains largely unknown. Here we investigate the role of the Tropics in this predictability. We show high levels of skill in tropical rainfall predictions, particularly over the Pacific but also the Indian and Atlantic Ocean basins. Rainfall fluctuations in these regions are associated with clear signatures in tropical and extratropical atmospheric circulation that are approximately symmetric about the Equator in boreal winter. We show how these patterns can be explained as steady poleward propagating linear Rossby waves emanating from just a few key source regions. These wave source ‘hotspots’ become more or less active as tropical rainfall varies from winter to winter but they do not change position. Finally, we show that predicted tropical rainfall explains a highly significant fraction of the predicted year-to-year variation of the winter North Atlantic Oscillation.