We present the Hybrid Hydrological Carbon Cycle Model (H2CM)—a global model that couples the terrestrial water and carbon cycles by integrating a process-informed deep learning approach with observational constraints for the water and carbon cycles. H2CM extends the hybrid hydrological model with vegetation (H2MV) to represent key terrestrial carbon fluxes, including gross primary productivity (GPP), autotrophic and heterotrophic respiration at daily resolution and 1-degree spatial scale. H2CM uses neural networks to learn and predict ecosystem properties governing water and carbon fluxes, such as carbon and water use efficiencies and basal respiration rate. H2CM uniquely combines multiple observational constraints synergistically: on top of hydrological and vegetation data constraints on terrestrial water storage variations, snow water equivalent, evapotranspiration, runoff and fraction of photosynthetically active radiation, the carbon cycle is informed by an observation-based GPP product, and net ecosystem exchange (NEE) from satellite and in-situ based atmospheric <em>CO</em><sub>2</sub> inversion datasets. H2CM reproduces the seasonal and interannual dynamics of carbon fluxes well. H2CM outperforms both purely data-driven models as well as state-of-the-art process-based model ensembles in capturing NEE seasonality, especially in challenging regions such as the South American tropics and Southern Africa. Moreover, H2CM reveals emergent spatial patterns in precipitation use efficiency, light use efficiency, and water-carbon coupling, consistent with empirical ecological understanding. Notably, we show that H2CM learns to represent the rain pulse effect on respiration in dry regions, which is often not well reproduced by global models. H2CM represents a key step toward a new generation of hybrid land surface models, with planned extensions to include the energy cycle.