A work-implement external-shape measurement system including a measurement controller that measures an external shape of a work implement provided to a work machine, the work-implement external-shape measurement system comprising: an image-capturing device that captures an image of a side surface of the work implement, characterized in that the measurement controller is configured to extract a contour line of the work implement on the image of the side surface of the work implement, the image being captured by the image-capturing device, compute a position of a plane representing the side surface of the work implement in an image-capturing-device coordinate system that is a three-dimensional coordinate system set for the image-capturing device, the position being computed on a basis of the image, and an internal parameter of the image-capturing device, on a basis of information on a position of any pixel on the contour line of the work implement on the image and the position of the plane, compute a coordinate value of a point on the contour line of the work implement in the image-capturing-device coordinate system, the point corresponding to the any pixel, and convert the coordinate value of the point on the contour line of the work implement in the image-capturing-device coordinate system, the point corresponding to the pixel, to a coordinate value in a work-implement coordinate system that is a two-dimensional coordinate system set for the work implement, and output the coordinate value of the point on the contour line of the work implement in the work-implement coordinate system to a work-machine controller of the work machine. an image-capturing device that captures an image of a side surface of the work implement, characterized in that the measurement controller is configured to extract a contour line of the work implement on the image of the side surface of the work implement, the image being captured by the image-capturing device, compute a position of a plane representing the side surface of the work implement in an image-capturing-device coordinate system that is a three-dimensional coordinate system set for the image-capturing device, the position being computed on a basis of the image, and an internal parameter of the image-capturing device, on a basis of information on a position of any pixel on the contour line of the work implement on the image and the position of the plane, compute a coordinate value of a point on the contour line of the work implement in the image-capturing-device coordinate system, the point corresponding to the any pixel, and convert the coordinate value of the point on the contour line of the work implement in the image-capturing-device coordinate system, the point corresponding to the pixel, to a coordinate value in a work-implement coordinate system that is a two-dimensional coordinate system set for the work implement, and output the coordinate value of the point on the contour line of the work implement in the work-implement coordinate system to a work-machine controller of the work machine. compute a coordinate value of a point on the contour line of the work implement in the image-capturing-device coordinate system, the point corresponding to the any pixel, and convert the coordinate value of the point on the contour line of the work implement in the image-capturing-device coordinate system, the point corresponding to the pixel, to a coordinate value in a work-implement coordinate system that is a two-dimensional coordinate system set for the work implement, and output the coordinate value of the point on the contour line of the work implement in the work-implement coordinate system to a work-machine controller of the work machine.