Robotic colonoscopes have been extensively developed for providing alternative solutions to conduct colon screening. Nevertheless, most robotic colonoscopes are still facing the challenge of unintuitive and difficult manipulation, particularly in the process of navigation, which may lead to long procedure duration and high workloads for surgeons. To tackle this problem, this article presents autonomous navigation of an electromagnetically actuated soft-tethered (EAST) colonoscope. By utilizing a deep-learning contour segmentation technique, a novel lumen center detection method combines both the contour and darkest region information of colon images to robustly and accurately estimate the center of the upcoming colon lumen, which provides heading directions for EAST colonoscope to navigate through the colon, while a navigation controller is developed to adjust the heading and locomotion velocity of EAST colonoscope accordingly. Comprehensive experiments are conducted to validate the effectiveness and efficacy of the developed lumen center detection model, with autonomous navigation of EAST colonoscope successfully demonstrated in both a commercialized colon phantom and an ex vivo porcine colon. A user study is conducted to verify the effectiveness of our proposed autonomous endoscopic navigation solution in shortening procedure duration and reducing surgeon workloads. The proposed methods are open source and can also be applied to other robotic colonoscopes, which can promote the clinical translation of robotic colonoscopy.