Terrestrial ecosystems play a vital role in mitigating climate change by absorbing a substantial fraction of anthropogenic CO2 emissions, with net ecosystem exchange (NEE) serving as a critical metric of land-atmosphere carbon flux. While individual climate variables like temperature, precipitation, and radiation are well-studied drivers of NEE, their interactions in multivariate contexts remain poorly understood. This study leverages the O-Information framework to disentangle the synergistic and redundant contributions of temperature, precipitation, vapour pressure deficit (VPD), terrestrial water storage, and photosynthetically active radiation (PAR) to NEE variability. Analysing global and regional dynamics, we reveal the nature of multivariate interactions governing NEE. Globally, pairs like VPD-PAR consistently exhibit synergy, underscoring their complementary roles in driving carbon exchange, while T-VPD and T-terrestrial water storage interactions are predominantly redundant. Regional analyses highlight distinct patterns of information sharing: temperate forests and semiarid regions are synergy-dominated, whereas tropical ecosystems and Arctic regions exhibit unique spatial variability in synergy and redundancy. These findings advance our understanding of how complex climate-ecosystem interactions shape carbon fluxes and offer insights for improving predictive models of NEE under changing climatic conditions.