Breckinridge was born in the District of Columbia and received his bachelors and law degrees from the University of Kentucky. He was admitted to the Kentucky Bar in 1940 and practiced law in Lexington, Kentucky. He worked in the Anti-Trust Division of the United States Department of Justice in 1940-1941 and served in United States Army during World War II, 1941-1946, rising to the rank of lieutenant colonel. Breckinridge was twice elected to the Kentucky House of Representatives and served there 1956-1960.

Breckinridge was elected Attorney General of Kentucky in 1959 when Bert T. Combs led the Democratic ticket to victory. He served his first term in that office 1960-1964. In that first term Breckinridge served on the National Conference of Commissioners on Uniform State Law and was a delegate to the Democratic National Convention in 1960. Under state law at that time Breckinridge could not run for a second consecutive term as Attorney General. He ran that year for Lieutenant Governor of Kentucky but lost in the Democratic primary to Harry Lee Waterfield. After that defeat Breckinridge returned to his law practice and began planning for a return to public office.

Breckinridge was elected to a second, non-consecutive term as Attorney General of Kentucky in 1967. Breckinridge won the office despite that fact that the Republican ticket, led by Louie B. Nunn, won the governorship and the office of secretary of state. Breckinridge served his second term as Attorney General of Kentucky 1968-1972. As his second term wound down Breckinridge again ran for Lieutenant Governor of Kentucky in 1971 but lost again in the Democratic primary, this time to the Speaker of the Kentucky House of Representatives, Julian Carroll.

In 1972 Breckinridge was elected to the United States House of Representatives from Kentucky's Sixth Congressional District (Lexington and the central Bluegrass). He defeated Republican Laban P. Jackson for the seat. He was re-elected in 1974 and 1976 and served in the House January 3, 1973 through January 3, 1979. Breckinridge ran for a fourth term in the House in 1978 but was defeated in the Democratic primary by Tom Easterly who in turn lost the seat to Republican Larry Hopkins.

After his defeat Breckinridge returned to the practice of law in Lexington, Kentucky where he died less than a year later on July 29, 1979. His ashes were interred at Lexington Cemetery.

As a member of the Kentucky House of Representatives and the United States House of Representatives Breckinridge was regarded as an independent moderate.

John B. Breckinridge hailed from the politically famous Breckinridge family. He was the great-great-grandson of John Breckinridge, who had served as the second ever Attorney General of Kentucky and in the Kentucky House of Representatives just like his descendant but who also served as a member of the United States Senate and as Attorney General of the United States. John B. Breckinridge was also the great-nephew of William Campbell Preston Breckinridge who also represented Kentucky in the United States House of Representatives.