We characterize the radii and masses of the star and planets in the Kepler-59 system, as well as their orbital parameters. The star parameters are determined through a standard spectroscopic analysis, resulting in a mass of and a radius of . The obtained planetary radii are for the inner and for the outer planet. The orbital parameters and the planetary masses are determined by the inversion of Transit Timing Variations (TTV) signals. We consider two different data sets: one provided by Holczer et al. , with TTVs only for Kepler-59c, and the other provided by Rowe et al. , with TTVs for both planets. The inversion method applies an algorithm of Bayesian inference (MultiNest) combined with an efficient N-body integrator (Swift). For each of the data set, we found two possible solutions, both having the same probability according to their corresponding Bayesian evidences. All four solutions appear to be indistinguishable within their 2-σ uncertainties. However, statistical analyses show that the solutions from Rowe et al. data set provide a better characterization. The first solution infers masses of and for the inner and outer planet, respectively, while the second solution gives masses of and . These values point to a system with an inner super-Earth and an outer mini-Neptune. A dynamical study shows that the planets have almost co-planar orbits with small eccentricities (e < 0.1), close to the 3:2 mean motion resonance. A stability analysis indicates that this configuration is stable over million years of evolution.