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Abstract Compound climate hazards, such as co-occurring temperature and precipitation extremes, substantially impact people and ecosystems. Internal climate variability combines with the forced global warming response to determine both the magnitude and spatial distribution of these events, and their consequences can propagate from one country to another via many pathways. We examine how exposure to compound climate hazards in one country is transmitted internationally via agricultural trade networks by analyzing a large ensemble of climate model simulations and comprehensive trade data of four crops (i.e. wheat, maize, rice and soya). Combinations of variability-driven climate patterns and existing global agricultural trade give rise to a wide range of possible outcomes in the current climate. In the most extreme simulated year, 20% or more of the caloric supply in nearly one third of the world’s countries are exposed to compound heat and precipitation hazards. Countries with low levels of diversification, both in the number of suppliers and the regional climates of those suppliers, are more likely to import higher fractions of calories (up to 93%) that are exposed to these compound hazards. Understanding how calories exposed to climate hazards are transmitted through agricultural trade networks in the current climate can contribute to improved anticipatory capacity for national governments, international trade policy, and agricultural-sector resilience. Our results highlight the need for concerted effort toward merging cutting-edge seasonal-to-decadal climate prediction with international trade analysis in support of a new era of anticipatory Anthropocene risk management.