In June, 1950, Drago graduated with a BS degree in chemistry from the University of Massachusetts Amherst. After he completed his time with the U.S. Air Force, he enrolled at Ohio State University under the GI bill, completing his Ph.D. degree on December 17, 1954, under Professor Harry Sisler. His thesis was entitled "Studies on the Synthesis of Chloramine and Hydrazine."
In 1955, he was hired at the University of Illinois at Urbana–Champaign Department of Chemistry, where he remained until 1982. In 1966, he published the textbook Physical Methods in Inorganic Chemistry.  In 1982, he moved to the University of Florida as Graduate Research Professor of Chemistry.