Burke is a lifelong resident of Chicago. His father, Joseph P. Burke, was a Cook County Sheriff's policeman who worked as a court bailiff. Joseph Burke served as committeeman from the 14th Ward (a local Democratic party post), and was elected alderman from the 14th Ward in November 1953.
Ed Burke attended Visitation Grammar School in Visitation Parish on Chicago's South Side and is a 1961 graduate of Quigley Preparatory Seminary. He graduated with a bachelor's degree from DePaul University in 1965, then worked for three years as a Chicago police officer, assigned to the state's attorney's office. Meanwhile, he studied law at DePaul University College of Law. In 1968, Burke received a Juris Doctor degree, was admitted to the Illinois Bar, and married his wife, Anne Marie.
While in law school in the late 1960s, an era of escalation in the Vietnam War, Burke received a draft deferment as a full-time student. After his marriage and the death of his father, he applied for and was granted a hardship deferment (3-A), as the sole support of his wife, mother, and two younger brothers. In June 1969, the Illinois Selective Service board of appeals reclassified him 1-A ("available for unrestricted military service"). At the same time, he was accepted into a Chicago-based United States Army Reserve unit, the 363rd civil affairs group, as a private. Political rivals expressed concern that special consideration allowed Burke to join the Reserve unit ahead of others, but an Army investigation found no evidence of manipulation in his favor.