Joint probabilistic models (JPMs) for the environmental parameters such as wave, wind, and current are nowadays of paramount importance in order to perform the reliability analysis of marine structures. These JPMs are also essential for long-term statistics-based design of offshore structures and to perform dynamic response analysis of floating units that are strongly dependent on the directionality of the environmental actions such as turret-moored floating, production, storage, and offloading vessels (FPSOs). Recently, some JPMs have been proposed in literature to represent the joint statistics of a reduced number of environmental parameters. However, it is a difficult task to obtain practical and reliable models to express the complete statistical dependence among the environmental parameters intensities and their correspondent directions. This paper presents a methodology, based on the Nataf transformation, to create a JPM of wave, wind, and current environmental parameters taking into account, also, the statistical correlation between intensities and directions. The proposed model considers ten short-term environmental variables: the significant wave height, peak period, and direction of the sea waves, the significant wave height, peak period, and direction of the swell waves, the amplitude and direction of the 1 h wind velocity, and, finally, the amplitude and direction of the surface current velocity. The statistical dependence between them is modeled using concepts of linear-linear, linear-circular, and circular-circular variables correlation. Some results of the proposed JPM methodology are presented based on simultaneous environmental data gathered in an offshore Brazil location.