Kraus was born in Las Palmas de Gran Canaria, Gran Canaria, Spain. He began his musical career at the age of four taking up piano lessons, singing in the school choir by age eight.

In 1956, Kraus made his professional operatic debut in Cairo as the Duke in Rigoletto, which became one of his signature roles. The following year, he sang in Alfredo at the Teatro Nacional São Carlos in Lisbon in a production of La Traviata with Maria Callas, a live recording of which was later released.

Kraus made his Covent Garden debut as Edgardo in Lucia di Lammermoor in 1959 and his La Scala debut as Elvino en La Sonnambula in 1960. He made his U.S. debut with Lyric Opera of Chicago 1962 and his Metropolitan Opera debut in 1966 in Rigoletto.

Kraus came to be virtually synonmous with such lyric tenor roles as Faust, Nemorino, Werther, Arturo and Don Ottavio. Thanks to his superlative technique and careful husbanding of his vocal resources, Kraus sang onstage well into his early 70s.

Kraus was also known for his performances of lighter music, notably zarzuela.

Due to his admirable technique and his extremely refined musicianship, accompanied by a seemingly effortless high register (he is one of the few tenors to achieve a high D in the most infamouos aria of Bellini's opera, I Puritani), many opera connoisseurs consider him to be one of the best tenors of the end of the 20th century. Several interviews with Alfredo Kraus show him to be an intelligent man with a great deal of thought behind his artistic choices in his roles, an admirably cultivated musical education and an utter respect for his chosen profession that guided his choices so that his first priority was the integrity of his artistic interpretation of a piece and not to showcase his formidable range or technique. In 1991, Kraus was awarded the Prince of Asturias Award.