Owing to a growing awareness toward environmental impact, the use of safer and eco-friendly solvents like deep eutectic solvents (DESs), has recently undergone important growth in the pharmaceutical field, with regard to their application as non-aqueous liquid administration vehicles, since they do not carry the same risks of toxicity and handling as traditional organic solvents. Major attention has been given to the development of advantageous transdermal drug delivery systems, because of their ease of use and better acceptability. Here, we report the use of two different DESs, based on choline chloride, used as hydrogen bond acceptor (HBA), and ascorbic acid or propylene glycol, used as hydrogen bond donors (HBDs), able to enhance the solubility and the topical delivery of dapsone, representing a class IV drug. The interactions between the DESs’ components and the drug were studied by performing DSC, FT-IR, and NMR analysis of the eutectic systems and the pure drug, confirming the establishment of H-bonds between the drug and the DESs’ components. Diffusion and permeability studies, carried out in a Franz cell, showed an increase in permeability, highlighting the great potential of DESs as dissolution and permeation enhancers in the development of novel and more effective drug delivery systems in topical administration.