Catalyzes the cleavage of glutathione into 5-oxo-L-proline and a Cys-Gly dipeptide. Acts specifically on glutathione, but not on other gamma-glutamyl peptides. Allows utilization of gluthathione through subsequent cleavage of the Cys-Gly dipeptide by Cys-Gly metallodipeptidase DUG1. glutathione = 5-oxo-L-proline + L-cysteinylglycine kcat is 50.8 min(-1) for glutathione. Present with 1300 molecules/cell in log phase SD medium. Belongs to the gamma-glutamylcyclotransferase family. ChaC subfamily.