Azaryan became a member of the Soviet national men's gymnastics team and competed with them at the 1954 World Artistic Gymnastics Championships. Alongside Azaryan on the team was friend and fellow Armenian Hrant Shahinyan. The Soviet team won gold in the team competition and Azaryan himself won the gold medal in rings. Azaryan joined the rest of the Soviet team at the 1955 European Men's Artistic Gymnastics Championships one year later. Azaryan became the European Champion in rings. He came behind stablemate Boris Shakhlin in most of the competitions, including coming second to Shakhlin on the high bars and individual all-around. He also had a three-way tie with Shaklin and Helmut Bantz on the parallel bars, resulting in three gold medalists.