He won the gold medal at the 2012 Summer Olympics at the men's 56 kg event, setting an Olympic Record in the clean and jerk with 168 kg, all while competing in the B session. He became only the fifth man to ever clean and jerk three times his own body weight. At the men's 56 kg weightlifting event at the 2016 Summer Olympics in Rio de Janeiro, Om was a favorite to renew his gold from London. After breaking his own Olympic record with a lift of 169 kg, Om was surpassed by Long Qingquan and had to settle for the silver medal.
He won his first World Championships in 2013, one year removed from becoming Olympic Champion, by beating Long Qingquan by 2 kg. In 2014 he defended his title as World Champion by lifting 296 kg at the 2014 World Weightlifting Championships. His total was tied with second place Thạch Kim Tuấn but he won by virtue of a lighter body weight. Following his World Championship win in 2014 he was the heavy favorite to win his third World championship in a row. He ended up winning the gold medal at the 2015 World Weightlifting Championships in spectacular fashion, after trailing Wu Jingbiao by 8 kg in the snatch Om Yun-chol outlifted Wu Jingbiao by 8 kg in the clean and jerk setting a new world record clean and jerk of 171 kg. Their totals of 302 kg were tied, but yet again Om Yun-chol won by virtue of a lighter body weight. He did not compete in the 2017 World Weightlifting Championships due to the North Korean team issuing a boycott of the Championships. In 2018 the International Weightlifting Federation reorganized the categories and he competed in the newly created 55 kg, he won his fourth World Championships by a margin of 24 kg over the second-place finisher, while winning gold medals in all lifts. During the clean and jerk portion of the competition he set a new world record of 162 kg.
At the 2014 Asian Games he won the gold medal in the 56 kg, in the clean and jerk portion he set a new world record lift of 170 kg. His total of 298 kg was an Asian Record at the time of competition. At the next Asian Games in 2018 he was the favorite to win another gold medal at the Games. After finishing in second place after the snatch portion of the competition, 1 kg behind Thạch Kim Tuấn, he outlifted him by 8 kg in the clean and jerk portion of the competition securing his second Asian Games gold medal.