Future projections of global mean precipitation change (Delta P) based on Earth-system models have larger uncertainties than projections of global mean temperature changes (Delta T)(1). Although many observational constraints on Delta T have been proposed, constraints on Delta P have not been well studied(2-5) and are often complicated by the large influence of aerosols on precipitation(4). Here we show that the upper bound (95th percentile) of Delta P (2051-2100 minus 1851-1900, percentage of the 1980-2014 mean) is lowered from 6.2 per cent to 5.2-5.7 per cent (minimum-maximum range of sensitivity analyses) under a medium greenhouse gas concentration scenario. Our results come from the Coupled Model Intercomparison Project phase 5 and phase 6 ensembles(6-8), in which Delta P for 2051-2100 is well correlated with the global mean temperature trends during recent decades after 1980 when global anthropogenic aerosol emissions were nearly constant. Delta P is also significantly correlated with the recent past trends in precipitation when we exclude the tropical land areas with few rain-gauge observations. On the basis of these significant correlations and observed trends, the variance of Delta P is reduced by 8-30 per cent. The observationally constrained ranges of Delta P should provide further reliable information for impact assessments.