After completing his graduate studies, Brady taught at Tuskegee University from 1421 to 1920. Brady accepted a teaching position at Howard University in Washington, D.C., in 1920 and eventually became the Chair of Howard University's Chemistry Department. In 1927 he moved to Fisk University to chair the school's Chemistry department. He remained at Fisk for 25 years until his retirement in 1952. While serving as the chair for the Chemistry department at Fisk University, Brady founded the first ever graduate studies program at a Black College/University. After his retirement from Fisk, he taught at Tougaloo College in Jackson, Mississippi.