Abstract: This disclosure describes an apparatus for wrapping all exposed surfaces of a large annular coil, including its hollow cylindrical core, to prevent contamination and to prepare it for shipping. A pair of opposing robotic arms hand off or transfer a roll of wrapping material, such as paper or plastic, from a gripper on one arm to a gripper on the other arm. The arms travel around both ends of the coil, handing off the roll back and forth above the coil and in the center of its hollow core, as it is slowly rotated by a variable-speed coil roller. The speed of the coil roller is adjusted such that the wrap overlaps during each successive pass around the coil, thereby ensuring its sealed integrity. A compact variable-tensioning mechanism, inserted into the roll, maintains constant tension on the wrapping material to keep it taut while being pulled around the coil.