Adds a GMP to the 5'-end of tRNA(His) after transcription and RNase P cleavage. This step is essential for proper recognition of the tRNA and for the fidelity of protein synthesis. Also functions as a guanyl-nucleotide exchange factor/GEF for the MFN1 and MFN2 mitofusins thereby regulating mitochondrial fusion. By regulating both mitochondrial dynamics and bioenergetic function, it contributes to cell survival following oxidative stress. 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. Homotetramer. Interacts with MFN1 and MFN2; functions as a guanyl-nucleotide exchange factor/GEF for MFN2 and also probably MFN1. Belongs to the tRNA(His) guanylyltransferase family.