ATP + gamma-L-glutamyl-L-cysteine + glycine = ADP + glutathione + H(+) + phosphate Binds 1 magnesium or manganese ion per subunit. Sulfur metabolism; glutathione biosynthesis; glutathione from L-cysteine and L-glutamate: step 2/2. Glycosylation at Arg-256 by NleB enhances the glutathione synthetase activity, leading to an increase in glutathione production (PubMed:31974499). Glycosylation may promote C.rodentium survival in oxidative stress conditions (PubMed:31974499). Belongs to the prokaryotic GSH synthase family.