Wand was born in Elbertfeld and studied in Wupertal, Allenstein and Detmold. He studied composition with Philipp Jarnach and piano with Paul Baumgartner, but was largely self-taught as a conductor. He started his career in Cologne, where he was to stay for several decades, as a conductor of the Cologne Opera orchestra. From 1947 to 1974 he was conductor of the Gürzenich Orchestra. In 1948 he started teaching conducting at a music school in Cologne. From the early 1950s he guest conducted a number of orchestras, making his London debut in 1951 with the London Symphony Orchestra. In 1974, he left Cologne to conduct the WDR and NDR Symphony Orchestras. In 1982, Wand became chief guest conductor of the BBC Symphony Orchestra.
Wand was particularly associated with the music of Schubert and Bruckner, but he was also a devoted interpreter of contemporary music of such composers as Bernd Alois Zimmermann, Wolfgang Fortner, and Olivier Messiaen.
Wand also composed music, mostly songs with orchestral accompaniment and music for ballet. He was awarded the German Record Award, the German Record Critic's Prize, the Echo Award, the Diapason d'Or and the Hans von Bülow Medal.