There seems to be magnetic fields at all scales and epochs in our Universe, but their origin at large scales remains an important open question of cosmology. In this work we focus on the generation of magnetic fields in the intergalactic medium due to the photoionizations by the first galaxies, all along the Epoch of Reionization. Based on previous studies which considered only isolated sources, we develop an analytical model to estimate the mean magnetic energy density accumulated in the Universe by this process. In our model, without considering any amplification process, the Universe is globally magnetized by this mechanism to the order of, at least, several 10−18 G during the Epoch of Reionization (i.e. a few 10−20 G comoving).