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Systematic climate shifts have been linked to multidecadal variability in observed sea surface temperatures in the North Atlantic Ocean. These links are extensive, influencing a range of climate processes such as hurricane activity and African Sahel and Amazonian droughts. The variability is distinct from historical global-mean temperature changes and is commonly attributed to natural ocean oscillations. A number of studies have provided evidence that aerosols can influence long-term changes in sea surface temperatures, but climate models have so far failed to reproduce these interactions and the role of aerosols in decadal variability remains unclear. Here we use a state-of-the-art Earth system climate model to show that aerosol emissions and periods of volcanic activity explain 76 per cent of the simulated multidecadal variance in detrended 1860-2005 North Atlantic sea surface temperatures. After 1950, simulated variability is within observational estimates; our estimates for 1910-1940 capture twice the warming of previous generation models but do not explain the entire observed trend. Other processes, such as ocean circulation, may also have contributed to variability in the early twentieth century. Mechanistically, we find that inclusion of aerosol-cloud microphysical effects, which were included in few previous multimodel ensembles, dominates the magnitude (80 per cent) and the spatial pattern of the total surface aerosol forcing in the North Atlantic. Our findings suggest that anthropogenic aerosol emissions influenced a range of societally important historical climate events such as peaks in hurricane activity and Sahel drought. Decadal-scale model predictions of regional Atlantic climate will probably be improved by incorporating aerosol-cloud microphysical interactions and estimates of future concentrations of aerosols, emissions of which are directly addressable by policy actions. [ABSTRACT FROM AUTHOR]