Healthy diets are known for their co-benefits of reducing environmental impacts and enabling the same agricultural resources to feed a larger human population. The EAT-Lancet (healthy reference) diet allows for compound benefits to human health and the ecosystem. It is unclear, however, to what extent the requirements of the EAT-Lancet diet may be sustainably met at the global scale. Here we combine a spatially distributed agro-hydrological model with a linear optimization analysis to relocate crops, minimizing, at the country scale, the irrigation-water consumption while improving the worldwide achievement of the EAT-Lancet nutritional goals. To that end, we define six dietary scenarios based on country-specific dietary habits from religion-related traditions, and existing livestock production systems, maintaining the same agricultural trade patterns (import-export relations). Our results suggest that an optimized global cropland allocation, and an adjustment in trade flows, would allow the global population to be fed with the EAT-Lancet diet, with a global reduction of the cultivated area of 37-40%, irrigation-water consumption of 78% (+/- 3%), and unsustainably irrigated areas of 22%. The adoption of the EAT-Lancet diet increases the global food trade share of global food production, measured in kilocalories, from 25% (baseline) to 36% (+/- 2%). The transition towards a sustainable food system that enhances the adoption of healthy diets globally is an urgent challenge. A study shows how the EAT-Lancet diet requirement could be met through sustainable agricultural strategies reducing land and water constraints.