The rapid expansion of artificial intelligence (AI)-enabled systems and cryptocurrency mining poses significant challenges to climate sustainability due to energy-intensive operations relying on fossil-powered grids. This work investigates the strategic coupling of AI data centers and cryptocurrency mining through shared energy infrastructure including colocated renewable power installations, battery energy storage, green hydrogen infrastructure, and carbon offsetting measures to achieve cost-effective and climate-neutral operations. Employing a novel energy systems modeling framework, it explores synergistic AI-crypto operations with a detailed scenario design along with an optimization modeling framework to assess the decarbonization potential and economic implications, enabling a transformative shift in the digital landscape. The results indicate that synergizing the AI-crypto operations while achieving net-zero targets can avoid up to 0.7 Gt CO2-equiv through 2030. Moreover, reaching these targets with synergistic strategies globally requires up to 90.7 GW of solar power and 119.3 GW of wind power capacity. The findings advocate for robust policy measures that facilitate the strategic expansion of synergistic AI-crypto operations including carbon credit schemes tailored for the digital sector, incentives for energy efficiency improvements, and international collaborations to bridge economic disparities. Future research should focus on refining strategic interventions across different geopolitical contexts to enhance global applicability.