Cochran was born in Webster Groves, Missouri; his father and maternal grandparents were Irish immigrants.

Cochran studied law and was admitted to the bar in 1921 at St. Louis, Missouri, but did not engage in extensive practice.

Cochran did not seek renomination in 1934, but ran unsuccessfully against Harry S. Truman for the Democratic nomination for U.S.

Cochran died in St. Louis, Missouri, on March 6, 1947, and was interred in Calvary Cemetery.

The John Cochran Veterans Medical Center in St. Louis is named in his behalf.