Ghiaurov was born in the small mountain town Velingrad in southern Bulgaria. As a child, he learned to play the violin, piano and clarinet. He began his musical studies at the Sofia Musical Academy in 1949. From 1950 to 1955, he studied at the Moscow Conservatory.
Ghiaurov made his operatic debut in 1955 as Don Basilio in Rossini's The Barber of Seville in Sofia. He made his Italian operatic debut in 1957 in Teatro Comunale Bologna, before starting an international career with his rendition of Varlaam in the opera Boris Godunov at La Scala in 1960.
He made his US debut in Gounod's Faust in 1963 at the Lyric Opera of Chicago, and he went on to sing twelve roles with the company, including the title roles in Boris Godunov, Don Quichotte, and Mefistofele.
Ghiaurov made his Metropolitan Opera debut in 1965 as Mephistopheles. He sang a total of eighty-one performances in ten roles there, last appearing there in 1996, as Sparafucile in Rigoletto. During the course of his career, he also performed at Moscow's Bolshoi Theatre, the Vienna State Opera, and Covent Garden.