Directional detection is a promising Dark Matter search strategy. Indeed, WIMP-induced recoils would present a direction dependence toward the Cygnus constellation, while background-induced recoils exhibit an isotropic distribution in the galactic rest frame. Taking advantage on theses characteristic features and even in the presence of a sizeable background, it has recently been shown that data of forthcoming directional detectors could lead either to a competitive exclusion or to a conclusive discovery, depending on the value of the WIMP-nucleon cross section. However, it is possible to further exploit these upcoming data by using the strong dependence of the WIMP signal with : the WIMP mass and the WIMP velocity distribution. Within the framework of a model independent method and by using a Markov Chain Monte Carlo analysis of recoil events, we show the possibility to constrain the unknown WIMP parameters, both from particle physics (mass and cross section) and galactic halo (velocity dispersion along the three axis), leading to an identification of non-baryonic Dark Matter.