An observed southward shift in tropical rainfall over land between 1950 and 1985, followed by a weaker recovery post-1985, has been attributed to anthropogenic aerosol radiative forcing and cooling of the Northern Hemisphere relative to the Southern Hemisphere. We might therefore expect models that have a strong historic hemispheric contrast in aerosol forcing to simulate a further northward tropical rainfall shift in the near-term future when anthropogenic aerosol emission reductions will predominantly warm the Northern Hemisphere. We investigate this paradigm using a perturbed parameter ensemble (PPE) of transient coupled ocean–atmosphere climate simulations that span a range of aerosol radiative forcing comparable to multi-model studies. In the 20th century, in our single-model ensemble, we find no relationship between the magnitude of pre-industrial to 1975 inter-hemispheric anthropogenic aerosol radiative forcing and tropical precipitation shifts. Instead, tropical precipitation shifts are associated with major volcanic eruptions and are strongly affected by internal variability. However, we do find a relationship between the magnitude of pre-industrial to 2005 inter-hemispheric anthropogenic aerosol radiative forcing and future tropical precipitation shifts over 2006 to 2060 under scenario RCP8.5. Our results suggest that projections of tropical precipitation shifts will be improved by reducing aerosol radiative forcing uncertainty, but predictive gains may be offset by temporary shifts in tropical precipitation caused by future major volcanic eruptions.