Burge was born in Evanston, Illinois and studied at the Eastman School of Music and in Florence. He first gained recognition in the 1960s, and in the early 1970s George Crumb wrote his books of piano pieces Makrokosmos for him. He recorded the work, and received a Grammy nomination.
In early 2002, Burge and Crumb were appointed to a joint residency at Arizona State University.