Solubility is a ubiquitous phenomenon in many aspects of material science. While solubility can be determined by considering the cohesive forces in a liquid via the Hansen solubility parameters (HSP), quantitative structure-property relationship models are often used for prediction, notably due to their low computational cost. Herein, we report gpHSP, an interpretable and versatile probabilistic approach to determining HSP. Our model is based on Gaussian processes (GP), a Bayesian machine learning approach that provides uncertainty bounds to prediction. gpHSP achieves its flexibility by leveraging a variety of input data, such as SMILES strings, COSMOtherm simulations, and quantum chemistry calculations. gpHSP is built on experimentally determined HSP, including a general solvents set aggregated from literature, and a polymer set experimentally characterized by this group of authors. In all sets, we obtained a high degree of agreement, surpassing well-established machine learning methods. We demonstrate the general applicability of gpHSP to miscibility of organic semiconductors, drug compounds and in general solvents, which can be further extended to other domains. gpHSP is a fast and accurate toolbox, which could be applied to molecular design for solution processing technologies.