Achieving healthy food systems will require regulation across the supply chain; however, binding international economic agreements may be constraining policy space for regulatory intervention in a way that limits uptake of 'best-practice' nutrition policy. A deeper understanding of the mechanisms through which this occurs, and under which conditions, can inform public health engagement with the economic policy sector. We conducted a realist review of nutrition, policy and legal literature to identify mechanisms through which international trade and investment agreements (TIAs) constrain policy space for priority food environment regulations to prevent non-communicable diseases (NCDs). Recommended regulations explored include fiscal policies, product bans, nutrition labelling, advertising restrictions, nutrient composition regulations, and procurement policies. The process involved 5 steps: initial conceptual framework development; search for relevant empirical literature; study selection and appraisal; data extraction; analysis and synthesis, and framework revision. Twenty-six studies and 30 institutional records of formal trade/investment disputes or specific trade concerns (STCs) raised were included. We identified 13 cases in which TIA constraints on nutrition policy space could be observed. Significant constraints on nutrition policy space were documented with respect to fiscal policies, product bans, and labelling policies in 4 middle-income country jurisdictions, via 3 different TIAs. In 7 cases, trade-related concerns were raised but policies were ultimately preserved. Two of the included cases were ongoing at the time of analysis. TIAs constrained policy space through 1) TIA rules and principles (non- discrimination, necessity, international standards, transparency, intellectual property rights, expropriation, and fair and equitable treatment), and 2) interaction with policy design (objectives framed, products/services affected, nutrient thresholds chosen, formats, and time given to comment or implement). Contextual factors of importance included: actors/institutions, and political/regulatory context. Available evidence suggests that there are potential TIA contributors to policy inertia on nutrition. Strategic policy design can avoid most substantive constraints. However, process constraints in the name of good regulatory practice (investor-state dispute settlement (ISDS), transparency, regulatory coherence, and harmonisation) pose a more serious threat of reducing government policy space to enact healthy food policies. © 2020 The Author(s); Published by Kerman University of Medical Sciences. This is an open-access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.