J. Herbert Burke was born in Chicago, Illinois, on January 14, 1913. He attended Northwestern University and earned a law degree from Chicago-Kent College of Law in 1940. He served in the Army during World War II, from 1942 to 1945, and received the Bronze Star and Purple Heart medals. He was discharged at the rank of captain and returned to Chicago to practice law for four years. Burke moved to Hollywood, Florida in 1949. In 1952, he was elected to the Broward County Commission, and went on to serve four terms.
In 1955 he was defeated in a campaign for a seat in the U.S. House of Representatives. In 1966, he was elected to his first term in the House. Burke served on the House Committee on International Relations, the Committee on House Administration, and the Select Committee on Narcotics Abuse and Control. In 1975, he was a member of the U.S. delegation to the United Nations. In 1978, after 11 years in the House, Burke lost his reelection bid a few months after he was arrested for public drunkenness and disorderly conduct in the parking lot of a nightclub in Dania, FL. Following his defeat, he retired to Falls Church, Virginia, and Fern Park, Florida. He died on June 16, 1993.