Turkevich was born on July 23, 1916, in Manhattan, New York, at the bishops house attached to Saint Nicholas Russian Orthodox Cathedral. His father, Leonid Turkevich, was dean at the time, and later became the Metropolitan of the Orthodox Church in North America. He had two brothers. Turkevich studied at Dartmouth College and obtained his bachelors degree in chemistry in 1937. He completed his Ph.D. at Princeton University on the structure of small molecules in 1940.