Agopoff was educated in Varna, Bulgaria, studying under Kiril Shivarov and George Nicholov, and served as an apprentice to his brother-in-law, the sculptor A. Massis. He then worked in Constantza, Rumania, for the Atelier Damien before coming to New York in 1929. He furthered his artistic studies at Columbia University and the National Academy of Design. For many years, he worked for sculptor Charles Keck.
Among his works are medals honoring Alexander Hamilton, Thomas Jefferson, Evangeline Booth, and J. Edgar Hoover. Other medals of Edwin Booth and William Cullen Bryant were designed for the New York University Hall of Fame; his memorial plaque of John F. Kennedy is at Hyannisport, Massachusetts. Agopoff's most unusual sculptural acheivment may be the carving of his home at Rock Ridge Lake, New Jersey, out of the live rock.
The sculptor began exhibiting at the Academy in 1943. He won the Academy's Daniel Chester French Medal in 1971 for his portrait of Edwin Thomas Booth. He was a member of the Allied Artists of America and of the National Sculpture Society.