Hudnut was born in Cincinnati, Ohio, on October 17, 1932. He attended the Darrow School in New Lebanon, New York, and graduated from Princeton University in 1954 with an A.B. in history and was elected to Phi Beta Kappa. As part of his undergraduate degree, Hudnut completed a senior thesis titled "Samuel Stanhope Smith: Enlightened Conservative." He earned a Master's Degree in Theology from the Union Theological Seminary in the City of New York and was ordained a clergyman in 1957.