We investigate the nature of high- z host galaxies of long Gamma-Ray Bursts ( LGRBs ) by means of state-of-the-art numerical simulations of cosmic structure formation and evolution of galaxies . We combine results from different runs with various box sizes and resolutions . By assigning to each simulated galaxy the probability to host a LGRB , assumed to be proportional to the mass of young stars , we provide a full description of the physical properties of high- z LGRB host galaxy population . We find that LGRBs at z > 6 are hosted in galaxies with typical star formation rates SFR \simeq 0.03 - 0.3 { M } _ { \odot } yr ^ { -1 } , stellar masses M _ { \star } \simeq 10 ^ { 6 } -10 ^ { 8 } ~ { } { M } _ { \odot } , and metallicities Z \simeq 0.01 - 0.1 { Z } _ { \odot } . Furthermore , the ratio between their doubling time and the corresponding cosmic time seems to be universally equal to \sim 0.1 - 0.3 , independently from the redshift . The distribution of their UV luminosity places LGRB hosts in the faint-end of the galaxy luminosity function , well below the current capabilities of space- or ground-based optical facilities . This is in line with recent reports of non-detection of LGRB hosts using extremely deep HST and VLT observations . In conclusion , high- z LGRBs are found to trace the position of those faint galaxies that are thought to be the major actors in the re-ionization of the Universe .