The self-assembly of amphiphilic molecules is a key process in numerous biological and chemical systems. When salts are present, the formation and properties of molecular aggregates can be altered dramatically by the specific types of ions in the electrolyte solution. We present a molecular thermodynamic model for the micellization of ionic surfactants that incorporates quantum dispersion forces to account for specific ion effects explicitly through ionic polarizabilities and sizes. We assume that counterions are distributed in the diffuse region according to a modified Poisson-Boltzmann equation and can reach all the way to the micelle surface of charge. Stern layers of steric exclusion or distances of closest approach are not imposed externally; these are accounted for through the counterion radial distribution profiles due to the incorporation of dispersion potentials, resulting in a simple and straightforward treatment. There are no adjustable or fitted parameters in the model, which allows for a priori quantitative prediction of surfactant aggregation behavior based only on the initial composition of the system and the surfactant molecular structure. The theory is validated by accurately predicting the critical micelle concentration (CMC) for the well-studied sodium dodecyl sulfate (SDS) surfactant and its alkaline-counterion derivatives in mono- and divalent salts, as well as the molecular structure parameters of SDS micelles such as aggregation numbers and micelle surface potential.