An agricultural harvester includes one or more actuators configured to move a crop unloading tube of the harvester relative to a frame of the harvester. Additionally, the agricultural harvester includes a sensor configured to capture data indicative of a presence of the crop receiving vehicle within a crop unloading zone of the agricultural harvester. Moreover, the agricultural harvester includes a computing system communicatively coupled to the sensor. As such, the computing system configured to determine when the crop receiving vehicle is present within the crop unloading zone based on the data captured by the sensor. In addition, when it is determined that the crop receiving vehicle is present within crop unloading zone, the computing system is configured to control an operation of the one or more actuators such that the crop unloading tube is moved relative to the frame from a current position to a predetermined crop unloading position.