The magnetic properties of (Ga,Mn)As thin films depend on both the Mn doping level and the carrier concentration. Using a post growth hydrogenation process, we show that it is possible to decrease the hole density from 1x10(21) cm(-3) to < 10(17) cm(-3) while keeping the manganese concentration constant. For such a series of films, we have investigated the variation of the magnetization, the easy and hard axes of magnetization, the critical temperatures, the coercive fields, and the magnetocrystalline anisotropy constants as a function of temperature, using magnetometry, ferromagnetic resonance, and magnetotransport measurements. In particular, we provided evidence that magnetic easy axes flipped from out-of-plane [001] to in-plane [100] axis, followed by the < 110 > axes, with increasing hole density and temperature. Our study concluded on a general agreement with mean-field theory predictions of the expected easy axis reversals, and of the weight of uniaxial and cubic anisotropies in this material.