Born in 1923 in Birsfelden, near Basel, Engel studied with Paul Baumgartner at the Basel Conservatory and with Alfred Cortot at the Ecole normale de musique in Paris, according to klassik.com; from 1956 to 1986 he was a professor at the Hochschule f‹r Musik und Theater in Hannover, Germany.
Among the renowned musicians with whom Engel collaborated, in concert and on disc, were cellist Pablo Casals, violinist Yehudi Menuhin, and singers Peter Schreier, Hermann Prey and Dietrich Fischer-Dieskau. He also recorded the complete piano music of Mozart and of Robert Schumann.