Scholars of international organisation commonly differentiate among three dimensions when studying the legitimacy of international institutions: input, throughput, and output legitimacy. I argue that the study of global governance needs to consider a fourth ‘face’ of legitimacy: constitutional legitimacy. This dimension addresses the normative and practical questions related to the constitutive justification for an institutional order – such as in whose name it is founded, whose interests it should serve, and how authority should be distributed within that institutional order. These questions are distinct from the procedural features of institutions emphasised by other dimensions and concern the constituent power that should ground the authority of governance institutions. In this article, I develop this fourth dimension of legitimacy, explore its varied expressions in world politics, and show how it has implications for the constitutional structure of global governance arrangements. I argue that different representations of constituent power shape the legitimacy of different authority relations within international institutions and illustrate these claims with an analysis of the politics of legitimacy in three cases: the ongoing effort to reform the UN Security Council, the negotiations over the founding of the International Criminal Court, and the debates over the Responsibility to Protect at the UN.