We present optical spectroscopy secured at the 10 m Gran Telescopio Canarias of the counterparts of 20 extragalactic γ-ray sources detected by the Fermi satellite. The observations allow us to investigate the nature of these sources and to determine their redshift. We find that all optical counterparts have a spectrum that is consistent with a BL Lac object nature. We are able to determine the redshift for 11 objects and set spectroscopic redshift limits for five targets. The optical spectrum is found featureless for only four sources. In the latter cases, we can set lower limits on the redshift based on the assumption that they are hosted by a typical massive elliptical galaxy whose spectrum is diluted by the nonthermal continuum. The observations allow us to unveil the nature of these gamma-ray sources and provide a sanity check of a tool to discover the counterparts of γ-ray emitters/blazars based on their multiwavelength emission.