With the development of large-scale data-driven research paradigm, spatially continuous and physically consistent gridded water-cycle data have become an essential basis for global hydrological process assessments, model training, and numerical simulations. Previous studies on terrestrial water budget closure have encountered persistent difficulty in simultaneously accounting for the observational realism of basin-scale runoff and the spatial continuity of gridded data. To address this problem, we developed a technical pathway for transferring constraints from real basin-scale observations to global gridded water-cycle variables. This approach overcomes the limitations of traditional basin-scale methods, which cannot adequately describe the internal spatial heterogeneity, and those of gridded-scale methods, which typically lack constraints from real runoff observations. The ISEA3H10 equal-area hexagonal discrete global grid was used as a unified spatial framework for this new dataset. Through basin–grid spatial overlay and area weighting, GRDC basin outlet runoff observations were converted into supervisory information that can be used by a gridded model. A deep-learning model with physical loss constraints was designed to jointly optimize key water-cycle variables, including precipitation, evapotranspiration, runoff, and terrestrial water storage change. The model further introduced natural background variables, including topography, vegetation, land-surface temperature, snow cover, and soil moisture. So that the water-cycle estimation does not rely solely on individual hydrological flux information, but also uses the spatial heterogeneity of more environmental factors to support water budget closure. This study integrated multiple remote-sensing, reanalysis, and land-surface model products, and further incorporated 710,274 GRDC runoff records from 3,471 basins worldwide as observational constraints. Based on these data, this study developed a monthly gridded dataset of precipitation, evapotranspiration, runoff, and terrestrial water storage changes covering global land areas from 2000 to 2020, for a total of 252 months. The optimized gridded runoff had a correlation coefficient of approximately 0.9 with GRDC observations, and its root mean square error (RMSE) was substantially lower than that of the original gridded runoff proxy products. Independent validation at 524 FLUXNET sites worldwide showed that precipitation and evapotranspiration maintained an accuracy comparable to, or more stable than, that of mainstream input products. Among 672 original <em>P-E-R-ΔS</em> product combinations, the combination exhibiting the optimal performance in terms of closure had a global monthly water budget residual RMSE of 43.37 mm/month. The optimized product reduced the RMSE to 14.33 mm/month, with a mean residual of −0.44 mm/month. The dataset preserved the seasonal consistency of each water-cycle variable and the consistency of the land-cover type zonal differences. Typical regions validation indicated that it also captured the coordinated anomalous responses of precipitation, evapotranspiration, runoff, and terrestrial water storage during special flood and drought events.