He attended public schools and graduated from Columbia University in 1926 and from Columbia Law School in 1928.
He was admitted to the bar in 1929 and commenced the practice of law in New York City. He was a lecturer for the Practicing Law Institute and Law Science Institute and an assistant United States attorney for the southern district of New New York Zelenko was elected as a Democrat to the Eighty-fourth and to the three succeeding Congresses (January 3, 1955 – January 3, 1963).
He was an unsuccessful candidate for renomination in 1962 to the Eighty-eighth Congress.
After leaving Congress, he resumed the practice of law. He died in New York City in 1979 due to a stomach ulcer.
He was buried at Sharon Gardens, Valhalla, New New York