1. An image processing apparatus for an electronic endoscope, comprising: an input unit to which an imaging signal captured by an electronic endoscope is input; an image processing unit that performs image processing on the imaging signal input from the input unit; an image display device that images an imaging signal, which has been subjected to the image processing by the image processing unit; and an output unit that outputs an imaging signal, which has been subjected to the image processing by the image processing unit, to the image display device, wherein the image processing unit performs first image processing in the case where a value of an aspect ratio of a display area of the image display device is larger than a value of an aspect ratio of a captured image indicated by the imaging signal, and performs second image processing in the case where the value of the aspect ratio of the display area of the image display device is equal to or less than the value of the aspect ratio of the captured image indicated by the imaging signal, and the first image processing is for making a magnification of an image of a peripheral portion outside a central portion of the captured image larger than a magnification of an image of the central portion so as to match the aspect ratio of the display area of the image display device, and the second image processing is for fixing a magnification of an entire area of the captured image so as to match the aspect ratio of the display area of the image display device.