Azaryan was awarded the Honoured Master of Sport of the USSR title in 1980.

Eduard started gymnastics in his early childhood under the guidance of his father, a three-time Olympic champion Albert Azaryan.

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.

Azaryan competed at the 1980 Summer Olympics in every artistic gymnastic event.

He won a gold medal in the team all-around.