Catalyzes the production of glutathione from gamma-glutamylcysteine and glycine in an ATP-dependent manner. Glutathione (gamma-glutamylcysteinylglycine, GSH) is the most abundant intracellular thiol in living aerobic cells and is required for numerous processes including the protection of cells against oxidative damage, amino acid transport, the detoxification of foreign compounds, the maintenance of protein sulfhydryl groups in a reduced state and acts as a cofactor for a number of enzymes. 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. Expressed ubiquitously. Belongs to the eukaryotic GSH synthase family.