Born in Oakland, California, Burke received an Artium Baccalaureus degree from Saint Mary's College of California in 1937 and a Bachelor of Laws from the UC Berkeley School of Law in 1940.

He was a deputy district attorney of Alameda County, California from 1940 to 1953, and was a Sergeant in the United States Army Infantry during World War II, from 1942 to 1946, remaining a United States Army Reserve Captain from 1946 to 1952.

[1] On June 27, 1958, Burke was nominated by President Dwight D. Eisenhower to a seat on the United States District Court for the Northern District of California vacated by Judge Oliver Deveta Hamlin Jr. Burke was confirmed by the United States Senate on July 21, 1958, and received his commission the same day.

[2][3] Burke continued to serve in a reduced capacity until his death of complications of pneumonia on March 15, 1988, in Oakland.

[1][3] He was the last district judge who continued to serve in active service appointed by President Eisenhower.