Adds a GMP to the 5'-end of tRNA(His) after transcription and RNase P cleavage. a 5'-end ribonucleotide-tRNA(His) + ATP + GTP + H2O = a 5'-end phospho-guanosine-ribonucleotide-tRNA(His) + AMP + 2 diphosphate + H(+) Binds 2 magnesium ions per subunit. Present with 1170 molecules/cell in log phase SD medium. Belongs to the tRNA(His) guanylyltransferase family.