Burke served in the United States Army during World War II.

In 1958 Burke was elected to the United States House of Representatives from Kentucky's 3rd District (Louisville).

Burke, a Democrat, was elected Mayor of Louisville that year, winning 48,337 votes to Republican John Porter Sawyer's 40,810.

Burke also increased garbage pickups and the sewers and pushed the construction of the Louisville Belvedere.

[1] Burke continued to practice law in Kentucky with Wyatt, Tarrant & Combs until 2005.