The Louisiana-born Anderson performed in relative obscurity until the tenor saxophonist's rise to prominence came in the 1990s.
Music companies began to release recordings of his work to favorable reviews and he became a regular on the jazz-festival circuit in the United States and Europe.
Anderson opened the Velvet Lounge in Chicago in 1982. At times, he did everything from collecting the $10 cover charge to jamming on stage to taking out the garbage.