The Atlantic multidecadal variability (AMV) – a basin-scale sea surface temperature (SST) fluctuation in the Atlantic – has dramatic influences on climate1–8. Understanding its causes has important social-ecological implications. However, the driver of AMV and its impacts remains debated because of limitations of current climate models9–13. Here we identify a systematic interhemispheric SST bias in the CMIP6 models that causes biased trends in large-scale atmospheric circulation and rainfall simulations. After removing the bias, we find the simulated AMV and associated impacts agree with observations. We show statistically and physically that AMV and its tropical impacts since 1950 have been driven primarily by anthropogenic aerosols and natural forcings, while internal dynamics likely drives them before 1950. We suggest using the tropical Atlantic SST contrast (dSST) as an AMV index because it naturally eliminates the global warming trend and can explain tropical impacts via a local Gill-type response. In the positive phase, this response features low-level westerly winds that enhance Sahel rainfall, high28 level easterly winds that affect vertical wind shear and hence North Atlantic Hurricanes, and a circum-global teleconnection that affects climate in other regions. Our results highlight that external forcing is responsible for the recent AMV, its widespread impacts, and the connection between the two.