The solubility of organic semiconductors in environmentally benign solvents is an important prerequisite for the widespread adoption of organic electronic appliances. Solubility can be determined by considering the cohesive forces in a liquid via Hansen solubility parameters (HSP). We report a numerical approach to determine the HSP of fullerenes using a mathematical tool based on artificial neural networks (ANN). ANN transforms the molecular surface charge density distribution (σ-profile) as determined by density functional theory (DFT) calculations within the framework of a continuum solvation model into solubility parameters. We validate our model with experimentally determined HSP of the fullerenes C60, PC61BM, bisPC61BM, ICMA, ICBA, and PC71BM and through comparison with previously reported molecular dynamics calculations. Most excitingly, the ANN is able to correctly predict the dispersive contributions to the solubility parameters of the fullerenes although no explicit information on the van der Waals forces is present in the σ-profile. The presented theoretical DFT calculation in combination with the ANN mathematical tool can be easily extended to other π-conjugated, electronic material classes and offers a fast and reliable toolbox for future pathways that may include the design of green ink formulations for solution-processed optoelectronic devices.