A system and method for automatic closure of sample vessels such as vessels with medical laboratory samples, having a plurality of identically shaped, stackable closure caps with a convex outer face and concave inner face that are stacked in a closure cap stack such that an upper closure cap in the stack bears with its convex outer face on the concave inner face of a lower closure cap lying immediately below in the stack. The system includes a closure gripper for gripping an uppermost closure cap from the stack, for transferring the gripped closure cap to the sample vessel to be closed, and for introducing the gripped closure cap into an opening of the sample vessel in order to tightly close the opening. The closure gripper has a centering piece insertable into a closure cap such that it bears on the concave inner face of the closure cap.