Watts recorded a variety of repertoire, concentrating on Romantic era composers such as Frédéric Chopin and Franz Liszt, but also including George Gershwin.

André spent his early childhood in Europe, living mostly near army posts where his father was stationed.

At age ten, Watts performed Mendelssohn's G minor concerto at the Robin Hood Dell outdoor amphitheater, where the Philadelphia Orchestra had given summer performances (from 1933 through 1975), and at fourteen, Franck's Symphonic Variations, again with the Philadelphia Orchestra.

[8] After the divorce of his parents in 1959, Watts remained with his mother,[9] who supported them by working as a secretary and later as a receptionist.

Watts enrolled at the Philadelphia Musical Academy (now a part of the University of the Arts), where he studied with Genia Robinor, Doris Bawden, and Clement Petrillo, graduating in June 1963.

Watts won the competition playing the first movement of Joseph Haydn's Piano Concerto in D.[9][10] At sixteen, Watts auditioned at Carnegie Recital Hall in a competition to play in conductor Leonard Bernstein's televised Young People's Concert series with the New York Philharmonic.

[9] On January 31, 1963, Bernstein asked the 16-year-old Watts to fill in for the ailing Glenn Gould, the scheduled soloist for the New York Philharmonic's regular subscription concert.

[5] Following graduation, Watts enrolled at the Peabody Institute in Baltimore, where he studied part-time for a Bachelor of Music degree with pianist Leon Fleisher.

In 1976, at age thirty, he celebrated his tenth consecutive appearance in the Lincoln Center Great Performers Series at Avery Fisher Hall.

[23] In 2004, Watts joined the faculty at Indiana University, where he held the Jack I. and Dora B. Hamlin Endowed Chair in Music.

[24][25] In 2019, Watts underwent surgery for a nerve injury to his left hand resulting in the cancellation of several performances.