Structural disorder inherent to amorphous materials affords them unique, tailorable properties desirable for diverse applications, but our ability to exploit these phenomena is limited by a lack of understanding of complex structure-property relationships. Here we focus on nonlinear optical absorption and derive a relationship between disorder and the two-photon absorption (2PA) coefficient. We employ an open-aperture Z-scan to measure the 2PA spectra of arsenic (III) sulfide (As2S3) chalcogenide glass films processed with two solvents that impart different levels of structural disorder. We find that the effect of solvent choice on 2PA depends on the energy of the exciting photons and explain this as a consequence of bonding disorder and electron state localization. Our results demonstrate how optical nonlinearities in As2S3 can be enhanced through informed processing and present a fundamental relationship between disorder and 2PA for a generalized amorphous solid.