Born and raised in Yerevan, Dzhigarkhanyan started acting in the academic and Russian theaters of the city, before moving to Moscow to continue stage acting. Since 1960, he appeared in a number of Armenian films. He became popular in the 1970s with the various roles he portrayed in Soviet films like "The New Adventures of the Elusive Avengers" (1968), its sequel "The Crown of the Russian Empire, or Once Again the Elusive Avengers" (1971) and "The Meeting Place Cannot Be Changed" (1979). After almost 30 years on the stage of the Mayakovsky Theatre, Dzhigarkhanyan taught at VGIK and in 1996 he founded his own drama theater in Moscow.