The surge in generative artificial intelligence (AI) may cause growing conflicts between securing electricity supplies and achieving sustainable development goals. Here, we propose off-grid hybrid wind-solar-storage (WSS) systems, which leverage the immense renewable resources in desert areas alongside relatively low-cost fiberoptic connectivity of data centers, to address this challenge. Using a global high-resolution techno-economic optimization model, we demonstrate that well-planned WSS systems can deliver cost-effective 24/7 uninterrupted power, primarily tailored for energy-intensive, latency-tolerant foundation model training. Furthermore, our analysis reveals that regions proximate to load centers can also support latency-sensitive inference tasks. This energy supply is capable of delivering 1 PWh globally in 2030 at levelized costs of around $39/MWh, meeting the forecasted electricity demand for AI by the International Energy Agency. Moreover, even if AI electricity demand increases 10-fold, reaching 10 PWh by 2030, the unit cost increment would be less than 20%. Further uncertainty analysis shows that under extreme investment (3.0×) and cooling (2.0×) cost assumptions for data centers operating with the desert WSS systems, this 10-PWh/yr demand could still be satisfied at competitive cost levels. The desert WSS systems could potentially align computational and clean energy infrastructure in the AI era, as well as simultaneously achieving decarbonization and ecological restoration.