The purpose of an excavator is to dig up materials and load them onto heavy-duty dump trucks. Typically, an excavator is positioned at the rear of the dump truck when loading. In order to automate this process, this paper proposes a system that employs a combined stereo camera and two LiDAR sensors to determine the three-dimensional (3D) position of the truck’s cargo box and to analyze its loading space. Sparse depth information acquired from the two LiDAR sensors is used to detect points on the door of the cargo box and establish the plane on its rear side. Dense depth information of the cargo box acquired from the stereo camera sensor is projected onto the plane of the box’s rear to estimate its initial 3D position. In the next step, the point cloud sampled along the long shaft of the edge of the cargo box is used as the input of the Iterative Closest Point algorithm to calculate a more accurate cargo box position. The data collected from the stereo camera are then used to determine the 3D position of the cargo box and provide an estimate of the volume of the load along with the 3D position of the loading space to the excavator. In order to demonstrate the efficiency of the proposed method, a mock-up of a heavy-duty truck cargo box was created, and the volume of the load in the cargo box was analyzed.