André Turp took private voice lessons with Édouard Woolley and Frank H. Rowe, before entering the Montreal Music Conservatory, where he was a pupil of Ruzena Herlinger. He was then awarded a grant and went to Italy to study with Hélène Vita. He made his stage debut in 1950 in operettas with the "Variétés Lyriques", in Montreal. He also took part in several programs with the Canadian Broadcasting Corporation.
His major breakthrough came in London, at the Royal Opera House, where he made his debut on February 5, 1960, as Edgardo in Lucia di Lammermoor, opposite Joan Sutherland. He was to appear with that company for several seasons in numerous roles including; the Duke of Mantua, Alfredo, Turridu, Rodolfo, Cavaradossi, etc. He was invited to the Glyndebourne Festival in 1961, where he sang in Henze's Elegy for Young Lovers.
At about the same time, he began a long association with the Opéra-Comique and the Palais Garnier, adding to his repertoire roles such as Werther (a role he sang with great success an estimated 500 times in Europe), Faust, Don Jose in Carmen, Hoffmann in Les contes d'Hoffmann, etc. He also appeared in Switzerland, Spain and Portugal.