Formylates methionyl-tRNA in mitochondria and the cytoplasm. Responsible for the formylation of the N-terminally formylated (Nt-formylated) mitochondrial matrix proteins that are encoded by mitochondrial DNA. Nt-formylated proteins in the cytoplasm are strongly up-regulated in stationary phase or upon starvation for specific amino acids and are targeted for degradation by an E3 ubiquitin ligase-mediated fMet/N-end rule pathway. Increased Nt-formylation of cytosolic proteins appears to be important for adaptation to these stresses. (6S)-10-formyltetrahydrofolate + L-methionyl-tRNA(fMet) = (6S)-5,6,7,8-tetrahydrofolate + H(+) + N-formyl-L-methionyl-tRNA(fMet) Belongs to the Fmt family.