Global food system analyses call for an urgent transition to sustainable human diets but how this might be achieved within the current global food regime is poorly explored. Here we examine the factors that have fostered major dietary shifts across eight countries in the past 70 years. Guided by transition and food-regime theories, we draw on data from diverse disciplines, reviewing post-World War 2 shifts in consumption of three food commodities: farmed tilapia, milk and chicken. We show that large-scale shifts in commodity systems and diets have taken place when public-funded technological innovation is scaled-up by the private sector under supportive state and international policy regimes, highlighting pathways between commodity systems transformation and food-system transitions. Our analysis suggests that the desired sustainability transition will require public policy leadership and private-sector technological innovation alongside consumers who culturally value and can afford healthy, sustainable diets.