- In 2000, sports journalists of Armenia recognized Albert Azaryan as the best Armenian sportsman of the 20th century.
- In 1962, based on the biography of Azaryan, the film Parqi oghakner (1962) was shot.
- The son of Albert Azaryan, Eduard Azaryan, as part of the USSR national team, was the champion of the Moscow Olympics in team competitions.
- Since the mid-fifties, the "cross" that Azaryan performed has been called the "Azaryan's Cross".
- Honorary Citizen of Erevan (2000).
- Azaryan was the strongest gymnast of his time in ring exercises.
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