Chaliapin grew up in a family who spoke three languages. He received an excellent education in Moscow and lived there until 1924, when he immigrated to Paris to be with his father, leaving behind his mother and the rest of the family. Chaliapin knew some of the greatest composers and conductors of the 20th century, particularly Rachmaninoff, a personal family friend and Teacher of his father. Tired of living in his father's Shadow in Paris, Chaliapin struck out on his own, moving to Hollywood to begin his film career — first in silent movies, in which his then-heavy accent would not be heard in the small bit parts he played. In his later years, Chaliapin achieved international stardom in more major roles.

In one of his briefest roles, Chaliapin dies in the arms of Gary Cooper in the opening scenes of For Whom the Bell Tolls (1943), based on Ernest Hemingway's 1940 novel. Regrettably he was never called on to play the part of Piotr Tchaikovsky, whom he resembled a great deal in his elder years.

Of Chaliapin's early film roles, one of the most memorable was in Victor Tourjansky's Prisoner of the Volga (1959). Much of his filmography lies in Italian films, including an appearance as Julius Caesar in Federico Fellini's film Roma.

Chaliapin was reunited with his mother, who then was 87 years old, in Rome in 1960. His mother's emigration was helped by the reforms (the so-called "thaw") of then Soviet Premier Nikita Khrushchev. The price of this was having to leave behind a museum-quality home and a magnificent art collection in Moscow as collected by Feodor Chaliapin, Sr. The only objects of art permitted to leave Russia were photograph albums of Chaliapin's childhood and youth in Moscow.

Chaliapin is perhaps most remembered by modern audiences for the film The Name of the Rose (1986), in which he played the venerable Jorge de Burgos. He had a major role in Inferno (1980). One of his most memorable roles was as the perplexed grandfather in Moonstruck (1987), starring Cher. The producers, in deciding whether to hire him for the role, sought the advice of Sean Connery, who is reputed to have said, "He's great, but he will steal the show." Chaliapin also played the role of Leonides Cox, Robert De Niro's father in Stanley & Iris (1990). His last notable film role was as Professor Bartnev in The Inner Circle (1991), a true story about Soviet Russia under the dictatorship of Joseph Stalin.

In 1992, Chaliapin died of natural causes after an illness in Rome, where he had lived since World War II. He was survived by his twin sister, Tatiana Chaliapin Chernoff, and several nieces and nephews.