BACKGROUND: Global constitutionalism is a way of looking at the world, at global rules and how they are made, as if there was a global constitution, empowering global institutions to act as a global government, setting rules which bind all states and people. ANALYSIS: This essay employs global constitutionalism to examine how and why global health governance, as currently structured, has struggled to advance the right to health, a fundamental human rights obligation enshrined in the International Covenant on Economic, Social and Cultural Rights. It first examines the core structure of the global health governance architecture, and its evolution since the Second World War. Second, it identifies the main constitutionalist principles that are relevant for a global constitutionalism assessment of the core structure of the global health governance architecture. Finally, it applies these constitutionalist principles to assess the core structure of the global health governance architecture. DISCUSSION: Leading global health institutions are structurally skewed to preserve high incomes countries' disproportionate influence on transnational rule-making authority, and tend to prioritise infectious disease control over the comprehensive realisation of the right to health. CONCLUSION: A Framework Convention on Global Health could create a classic division of powers in global health governance, with WHO as the law-making power in global health governance, a global fund for health as the executive power, and the International Court of Justice as the judiciary power.