J-PAS will soon start imaging 8000 deg2 of the northern sky with its unique set of 56 filters (R $sim$ 60). Before, we observed 1 deg2 on the AEGIS field with an interim camera with all the J-PAS filters. With this data (miniJPAS), we aim at proving the scientific potential of J-PAS to identify and characterize the galaxy populations with the goal of performing galaxy evolution studies across cosmic time. Several SED-fitting codes are used to constrain the stellar population properties of a complete flux-limited sample (rSDSS <= 22.5 AB) of miniJPAS galaxies that extends up to z = 1. We find consistent results on the galaxy properties derived from the different codes, independently of the galaxy spectral-type or redshift. For galaxies with SNR>=10, we estimate that the J-PAS photometric system allows to derive stellar population properties with a precision that is equivalent to that obtained with spectroscopic surveys of similar SNR. By using the dust-corrected (u-r) colour-mass diagram, a powerful proxy to characterize galaxy populations, we find that the fraction of red and blue galaxies evolves with cosmic time, with red galaxies being $sim$ 38% and $sim$ 18% of the whole population at z = 0.1 and z = 0.5, respectively. At all redshifts, the more massive galaxies belong to the red sequence and these galaxies are typically older and more metal rich than their counterparts in the blue cloud. Our results confirm that with J-PAS data we will be able to analyze large samples of galaxies up to z $sim$ 1, with galaxy stellar masses above of log(M$_*$/M$_{odot}$) $sim$ 8.9, 9.5, and 9.9 at z = 0.3, 0.5, and 0.7, respectively. The SFH of a complete sub-sample of galaxies selected at z $sim$ 0.1 with log(M$_*$/M$_{odot}$) > 8.3 constrain the cosmic evolution of the star formation rate density up to z $sim$ 3 in good agreement with results from cosmological surveys.