ArcheoTUI is a new tangible user interface for the efficient assembly of the 3D scanned fragments of fractured archeological objects. An efficient user interaction for the complex task to orientate or position two 3D objects relative to each other is essential, eventually in addition to automatic matching techniques. Our key idea is to use tangible props for the manipulation of the virtual fragments. In each hand, the user manipulates an electromagnetically tracked prop, and the translations and rotations are directly mapped to the corresponding virtual fragments on the display. For each hand, a corresponding foot pedal is used to clutch the movements of the hands. Hence, the user's hands can be repositioned, or the user can be switched. The software of ArcheoTUI is designed to easily change assembly hypotheses, beyond classical undo/redo, by using a scene graph. We designed ArcheoTUI on the demand of archeaologists and in a direct collaboration with them, and we conducted two user studies on site at their workplace. The first user study revealed that the interface, and especially the foot pedal, was accepted, and that all the users managed to solve simple assembly tasks. In a second user study, we compare a different clutching mechanism with buttons on the props to the foot pedal mechanism. This second user study revealed that the movement of the hands is more similar to real-world assembly scenarios when using the foot pedals, and that the users can keep on concentrating on the actual assembly task. Finally, we show how the virtual assembly is used for a fractured archeological finding.