Global hydrological models are important decision support tools for policy making in today’s water-scarce world as their process-based nature allows for worldwide water resources assessments under various climate-change and socio-economic scenarios. Although efforts are continuously being made to improve water resource assessments, global hydrological model computational demands have dramatically increased and calibrating them has proven to be difficult. To address these issues, deep-learning approaches have gained prominence in the hydrological community, in particular the development of deep-learning surrogates. Nevertheless, the development of deep-learning global hydrological model surrogates remains constrained, as previous surrogate frameworks only focus on land-surface fluxes for a single spatial resolution. Therefore, we introduce a global hydrological model surrogate framework that includes integrated spatially-distributed runoff routing, human impacts on water resources and the ability to scale across spatial resolutions. To test our framework we develop a deep-learning surrogate for the PCRaster Global Water Balance (PCR-GLOBWB) global hydrological model. Our surrogate performed well when compared to the model outputs, with a median Kling-Gupta Efficiency (KGE) of 0.45, while predictions were at least an order of magnitude faster. Moreover, the multi-resolution surrogate performed similarly to several single-resolution surrogates, indicating limited trade-offs between the surrogate’s broad spatial applicability and its performance. Model surrogates are a promising tool for the global hydrological modeling community, given their potential benefits in reducing computational demands and enhancing calibration. Accordingly, our framework provides an excellent foundation for the community to create their own multi-scale deep-learning global hydrological model surrogates.