Fluorogenic dyes such as FlAsH and ReAsH are used widely to localize, monitor, and characterize proteins and their assemblies in live cells. These bis-arsenical dyes can become fluorescent when bound to a protein containing four proximal Cys thiols-a tetracysteine (Cys4) motif. Yet the mechanism by which bis-arsenicals become fluorescent upon binding a Cys4 motif is unknown, and this nescience limits more widespread application of this tool. Here we probe the origins of ReAsH fluorogenicity using both computation and experiment. Our results support a model in which ReAsH fluorescence depends on the relative orientation of the aryl chromophore and the appended arsenic chelate: the fluorescence is rotamer-restricted. Our results do not support a model in which fluorogenicity arises from the relief of ring strain. The calculations identify those As-aryl rotamers that support fluorescence and those that do not and correlate well with prior experiments. The rotamer-restricted model we propose is supported further by biophysical studies: the excited-state fluorescence lifetime of a complex between ReAsH and a protein bearing a high-affinity Cys4 motif is longer than that of ReAsH-EDT2, and the fluorescence intensity of ReAsH-EDT2 increases in solvents of increasing viscosity. By providing a higher resolution view of the structural basis for fluorogenicity, these results provide a clear strategy for the design of more selective bis-arsenicals and better-optimized protein targets, with a concomitant improvement in the ability to characterize previously invisible protein conformational changes and assemblies in live cells.