The response of upper tropospheric clouds and relative humidity (RH) to warming is important to the overall sensitivity of the Earth to increasing greenhouse gas concentrations. Previous research has shown that changes in hydrologic fields should closely track rising isotherms in a warming climate. Here we show that the distribution of tropical clouds and RH in general circulation models is approximately constant under greenhouse warming when using temperature as a vertical coordinate. By assuming that these fields are an invariant function of atmospheric temperature and that temperature change follows a dilute moist adiabat, we are able to accurately predict cloud fraction and RH changes in the tropical upper troposphere (150–400 hPa) in 27 general circulation models. Our results indicate that intermodel spread in changes of tropical upper tropospheric clouds and RH is closely related to differences in model climatology and could be substantially reduced if model ensembles reliably reproduced observed climatologies.