This work deals with the problem of how the spreading of diseases depends on structural patterns. The study contributes to further advance our understanding of epidemic spreading processes by proposing a non-perturbative formulation of the heterogeneous mean field approach that has been commonly used in the physics literature to deal with this kind of spreading phenomena. We propose non-perturbative equations without making any assumption about the proximity of the system to the epidemic threshold, nor any linear approximation of the dynamics. In particular, we first develop a probabilistic description of the spreading of the disease at the node level for the so-called susceptible-infected-susceptible family of models, and after we derive the corresponding heterogeneous mean-field approach. This allows us to use the full extension of the approach instead of pruning the expansion to first order, which leads to a non-perturbative formulation that can be solved by fixed-point iteration, and used with reliability far away from the epidemic threshold to assess the prevalence of the epidemics. Our results are in close agreement with Monte Carlo simulations thus enhancing the predictive power of the classical heterogeneous mean field approach, while providing a more effective framework in terms of computational time.