ATP + gamma-L-glutamyl-L-cysteine + glycine = ADP + glutathione + H(+) + phosphate Binds 1 Mg(2+) or Mn(2+) ion per subunit. Inhibited by 7,8-dihydrofolate, methotrexate and trimethoprim. Sulfur metabolism; glutathione biosynthesis; glutathione from L-cysteine and L-glutamate: step 2/2. Homotetramer. Belongs to the prokaryotic GSH synthase family.