HIV-1 RNase H catalyzes the cleavage of the DNA/RNA hybrid bound to the HIV-1 RT enzyme dependent on a non-canonical DEDDh motif for coordination of two catalytic Mg 2+ ions. Our QM/MM calculations, in agreement with prior work, found that the reaction proceeds via two transition states that separate the two protonation events: (i) deprotonation of the nucleophilic water and (ii) protonation of the leaving group. Beyond this, here we identified a new proton transfer mechanism, both for the deprotonation of the nucleophilic water and for the protonation of the leaving group, that is able to account for the multitude of experimental results not only in RNase H but in many other nucleases. We identified a conserved histidine residue, which has a dual role as activator of the nucleophile and recruiter of a third divalent metal ion in the product complex. The histidine is structurally and functionally conserved across several other enzymes with a RNase or DNase function, and homologous mutational and computational studies in nucleases with a different positioning of the same active site residues (i.e the canonical DEDDh motif) support our mechanistic results. We highlight differences and similarities of the canonical DEDDh motif in 3'-5' exonucleases such as the subunit of polymerase III or RNase T with the non-canonical motif found in various RNases H in the discussion of our results.