Changes in the flow around the North Atlantic subtropical High (NASH) have important implications on the steering of Atlantic tropical cyclones (TCs). We find a significant enhancement of the NASH on interannual timescales (1970-2016) linked to an anomalously strong Indian monsoon in September. Consistent with a stronger NASH, enhanced anticyclonic flow and subtropical easterlies in the eastern Atlantic basin are found during strong monsoon years. Observational regression analysis combined with a statistical track model are used to assess the influence of these monsoon-linked wind variations on Atlantic TC tracks originating in the main development region (MDR). Even when controlling for the effects of El Niño Southern Oscillation (ENSO), a westward shift of TC tracks is shown to be robustly correlated to internal monsoon variability in September. This work highlights variability of the Indian monsoon as an additional constraint on Atlantic TCs, with potential implications for landfall probability.