Conjugates glutathione (gamma-Glu-Cys-Gly) and spermidine to form glutathionylspermidine in the biosynthesis trypanothione (N(1),N(8)-bis(glutathionyl)spermidine), which is involved in maintaining intracellular thiol redox and in defense against oxidants. ATP + glutathione + spermidine = ADP + glutathionylspermidine + H(+) + phosphate The N-terminus is blocked. In the C-terminal section; belongs to the glutathionylspermidine synthase preATP-grasp family.