Zuckert was born in New York City. He attended public elementary and high schools in suburban New York, received preparatory education at the Salisbury School, Salisbury, Connecticut, and earned his bachelor of arts degree from Yale University in 1933. Zuckert entered the combined Yale Law School-Harvard Business School course sponsored by William O. Douglas, who later served on the Supreme Court. That course, a pioneer experiment by Yale and Harvard, supplemented legal training with administration to foster an awareness of the business problems of clients. After graduation, Zuckert became a member of both the Connecticut and New York Bars. He later became a member of the Bar in the District of Columbia.