ATP + gamma-L-glutamyl-L-cysteine + glycine = ADP + glutathione + H(+) + phosphate Binds 1 Mg(2+) ion per subunit. Sulfur metabolism; glutathione biosynthesis; glutathione from L-cysteine and L-glutamate: step 2/2. Homodimer. Present with 3430 molecules/cell in log phase SD medium. Belongs to the eukaryotic GSH synthase family.