Yang's parents are Yang Gwan-gwon and Ki Suk-hyang. Their impoverished family previously lived in one of Gwangju's shantytowns, before relocating to North Jeolla Province's Gochang, in South Korea's countryside, in 2010, after his father, a construction worker, suffered from serious injuries. His family currently lives in a makeshift converted greenhouse constructed from PVC pipes. After Yang's father lost his job, Yang supported the family with a modest income from the Korea Gymnastic Association. Yang's coach Cho Sung-doe admitted that he had been unaware of the family's precarious financial situation before Yang won the gold medal.
Yang is the reigning vault champion at the Asian Games. In 2012, he became the first Korean gymnast to win Olympic gold in Gymnastics, winning the vault competition in London. In 2013, He won gold in vault at the 2013 Summer Universiade in Kazan, Russia. He is famous in the gymnastics world for performing the hardest vault in the world, a front handspring front layout with three twists. Yang is additionally working on a second difficult skill, but this vault is from a sideways entry.  He is also the reigning world champion, having won gold in the vault at both the 2011 and 2013 World Artistic Gymnastics Championships