Asparaginyl endopeptidases (AEPs) are a class of enzymes commonly associated with proteolysis in the maturation of seed storage proteins. However, a subset of AEPs work preferentially as peptide ligases, coupling release of a leaving group to formation of a new peptide bond. These "ligase-type" AEPs require only short recognition motifs to ligate a range of targets, making them useful tools in peptide and protein engineering for cyclisation of peptides or ligation of separate peptides into larger products. Here we report the recombinant expression, ligase activity and cyclisation kinetics of three new AEPs from the cyclotide producing plant Oldenlandia affinis with superior kinetics to the prototypical recombinant AEP ligase OaAEP1b. These AEPs work preferentially as ligases at both acidic and neutral pH and we term them "canonical AEP ligases" to distinguish them from other AEPs where activity preferences shift according to pH. We show that these ligases intrinsically favour ligation over hydrolysis, are highly efficient at cyclising two unrelated peptides and are compatible with organic co-solvents. Finally, we demonstrate the broad scope of recombinant AEPs in biotechnology by the backbone cyclisation of an intrinsically disordered protein, the 25 kDa malarial vaccine candidate Plasmodium falciparum merozoite surface protein 2 (MSP2).