Although global warming is expected to occur at approximately constant relative humidity, the latest IPCC report remains elusive about the magnitude of observed changes in tropospheric humidity and their attribution. Here we use a quality-controlled dataset of in situ observations, global reanalyses, and a long record of global mean surface temperature to constrain both recent and future changes in global mean total precipitable water. Most state-of-the-art global climate models tend to exaggerate the projected atmospheric moistening, in line with their overestimation of global warming and of the sensitivity of atmospheric humidity to both anthropogenic greenhouse gases and aerosols across the 20^th century. A 39% narrowing in the range of the projections is obtained after applying the observational constraints, with a best-guess estimate of + 7% per °C of global warming. This finding provides further evidence of a substantial intensification of the global water cycle as long as global warming continues.