Four on-lattice and six off-lattice models for active matter are studied numerically, showing that in contact with a wall, they display universal wetting transitions between three distinctive phases. The particles, which interact via exclusion volume only, move persistently and, depending on the model, change their direction either via tumble processes or rotational diffusion. When increasing the turning rate νT , the systems transit from total wetting, to partial wetting and dewetted phases. In the first phase, a wetting film covers the wall, with increasing heights while decreasing νT . The second phase is characterized by wetting droplets on the walls. And, finally, the walls dries with few particles in contact with it. These phases present two continuous non-equilibrium transitions. For the first transition, from partial to total wetting, the fraction of dry sites vanishes continuously when decreasing νT , with a power law of exponent 1. And, for the second transition, an order parameter proportional to the excess mass in droplets decreases continuously with a power law of exponent 3 when approaching a critical value of νT . The critical exponents are the same for all the models studied.