A protein complex composed of two or more polypeptide subunits, and which possesses glutathione synthase activity (catalysis of the reaction: L-gamma-glutamyl-L-cysteine + ATP + glycine = ADP + glutathione + 2 H(+) + phosphate). In eukaryotes, the complex is homodimeric, in E. coli glutathione synthase exists as a tetramer, and in S. pombe the complex exists as a homodimer or a heterotetramer.