Future hydroclimate projections from state-of-the-art climate models show large uncertainty and model spread, particularly in the tropics and over the monsoon regions. The precipitation and circulation responses to rising greenhouse gases involve a fast component associated with direct radiative forcing and a slow component associated with sea surface temperature (SST) warming; the relative importance of the two may contribute to model discrepancies. In this study, regional hydroclimate responses to greenhouse warming are assessed using output from coupled general circulation models in the Coupled Model Intercomparison Project-Phase 5 (CMIP5) and idealized atmospheric general circulation model experiments from the Atmosphere Model Intercomparison Project. The thermodynamic and dynamic mechanisms causing the rainfall changes are examined using moisture budget analysis. Results show that direct radiative forcing and SST change exert significantly different responses both over land and ocean. For most part of the Asian monsoon region, the summertime rainfall changes are dominated by the direct CO2 radiative effect through enhanced monsoon circulation. The response to SST warming shows a larger model spread compared to direct radiative forcing, possibly due to the cancellation between the thermodynamical and dynamical components. While the thermodynamical response of the Asian monsoon is robust across the models, there is a lack of consensus for the dynamical response among the models and weak multi-model mean responses in the CMIP5 ensemble, which may be related to the multiple physical processes evolving on different time scales.