DNA stores our genetic information and is ubiquitous in biological and biotechnological applications, where it interacts with binding partners ranging from small molecules to large macromolecular complexes. Binding is modulated by mechanical strains in the molecule and, in turn, can change the local DNA structure. Frequently, DNA occurs in closed topological forms where topology and supercoiling add a global constraint to the interplay of binding-induced deformations and strain-modulated binding. Here, we present a quantitative model of how the global constraints introduced by DNA topology modulate binding and create a complex interplay between topology and affinity. We focus on fluorescent intercalators, which unwind DNA and enable direct quantification via fluorescence detection. Using bulk measurements, we show that DNA supercoiling can increase or decrease intercalation relative to an open topology depending on ligand concentration and the initial topology. Our model quantitatively accounts for observations obtained using psoralen for UV-induced DNA crosslinking, which is frequently used to quantify supercoiling in vivo. Finally, we observe topology-dependent binding in a single-molecule assay, which provides direct access to binding kinetics and DNA supercoil dynamics. Our results have broad implications for the detection and quantification of DNA and for the modulation of DNA binding in cellular contexts.