Spears grew up in Detroit and studied at the Juilliard School. In 1974, while still a student, he joined the Alvin Ailey American Dancer Theater, where he remained for four years. Also in 1974, he also created his own company, the Spears Collection, which he led until 1983.
In 1984, Spears moved to Denmark and began choreographing for NDDT; he was the company's artistic director and resident choreographer from 1987 through 1999. Among his works for the company were full-evening dances based on the lives of such figures as writer Karen Blixen, jazz saxophonist Dexter Gordon, and writer A.A. Milne.
Spears also choreographed for the Royal Danish Ballet and for American companies including Philadanco, the Dallas Black Dancer Theater, and the Dayton Contemporary Dance Company.
The winner of the 1990 Copenhagen Dance Prize and of many grants, Spears was knighted by Queen Margrethe of Denmark in 2003.