A computationally-assisted and green spectrophotometric method has been developed for the determination of fostemsavir, a recently FDA-approved drug used in combination with antiretroviral drugs to treat multidrug-resistant HIV-1 infection. The method was developed using computational studies and solvent selection based on green chemistry principles. The density functional theory method was employed to identify bromophenol blue as the preferred acid dye for efficient extraction of fostemsavir. The solvent selection process involved a careful evaluation of the green ranking of solvents, which led to the use of water as the solvent. The method involved the extraction of fostemsavir with bromophenol blue to form a yellow ion-pair complex, which exhibited maximally sharp peaks at 418 nm, enabling sensitive visible spectrophotometric determination of fostemsavir in bulk and pharmaceutical preparations. The extraction procedures were optimized, and the method was demonstrated to be sensitive over the concentration range of 2–12 μg/mL fostemsavir. Furthermore, the method was evaluated with respect to green chemistry principles using the analytical eco-scale, the green analytical method index, and analytical greenness metric approach, all of which confirmed that the data obtained by the proposed method were environmentally acceptable.