Eduard started gymnastics in his early childhood under the guidance of his father, a three-time Olympic champion Albert Azaryan. In 1978, Eduard Azaryan became USSR champion in the team all-around and joined the USSR national gymnastics team. In the same year, Azaryan won a bronze medal at the World Cup in the individual all-around and a silver medal at the 1978 World Artistic Gymnastics Championships in the team all-around.