Improvements in agricultural production have drastically increased grain yields in the past half-century. Despite this growth in productivity and calories available per capita, malnutrition - both undernutrition and, increasingly, overweight - remains pervasive. Though nutrition is critical to human health, it has yet to be systematically integrated into assessments of agricultural and food systems. Using three complementary diversity metrics, we find strong associations between nutritional diversity of national food supplies and key human health outcomes, while controlling for socio-economic factors. For low-income countries the diversity of agricultural goods produced by a country is a strong predictor for food supply diversity; for middle- and high-income countries national income and trade are better predictors. Our results highlight the importance of diversity in national food systems for human health. We provide metrics for agricultural and food security policies to consider nutritional diversity.