Lytic polysaccharide monooxygenases (LPMOs) are widely distributed in Nature, where they catalyze the hydroxylation of glycosidic bonds in polysaccharides. Despite the importance of LPMOs in the global carbon cycle and in industrial biomass conversion, the catalytic properties of these monocopper enzymes remain enigmatic. Strikingly, there is a remarkable lack of kinetic data, likely due to a multitude of experimental challenges related to the insoluble nature of LPMO substrates, like cellulose and chitin, and to the occurrence of multiple side reactions. Here, we employed competition between well characterized reference enzymes and LPMOs for the H2O2 co-substrate to kinetically characterize LPMO-catalyzed cellulose oxidation. LPMOs of both bacterial and fungal origin showed high peroxygenase efficiencies, with kcat/KmH2O2 values in the order of 105-106 M-1 s-1. Besides providing crucial insight into the cellulolytic peroxygenase reaction, these results show that LPMOs belonging to multiple families and active on multiple substrates are true peroxygenases.