The generation of enantiodivergent biocatalysts for C-H oxyfunctionalizations is ever more important in modern synthetic chemistry. Here, we have applied the FuncLib algorithm based on phylogenetic and Rosetta calculations to design a diverse repertoire of active, stable, and enantiodivergent fungal peroxygenases. 24 designs, each carrying 4-5 mutations in the catalytic core, were expressed functionally in yeast and benchmarked against characteristic model compounds. Several designs were active and stable in a range of temperature and pH, displaying unprecedented enantiodivergence, changing regioselectivity from alkyl to aromatic hydroxylation, and increasing catalytic efficiencies up to 10-fold, with 15-fold improvements in total turnover numbers over the parental enzyme. We find that this dramatic functional divergence stems from beneficial epistasis among the mutations and an extensive reorganization of the heme channel. Our work demonstrates that FuncLib can rapidly design highly functional libraries enriched in enantioselective peroxygenases not seen in nature for a range of biotechnological applications.