Cooper was educated at the Dalton School, a co-educational independent school in New York City. At age 17, after graduating from the Dalton School a semester early, Cooper travelled around Africa for several months on a "survival trip". He contracted malaria on the trip and was hospitalized in Kenya. Describing the experience, Cooper wrote "Africa was a place to forget and be forgotten in." Cooper went on to attend Yale University, where he resided in Trumbull College, and was inducted into the Manuscript Society, majoring in political science and graduated in 1989.
During college, Cooper spent two summers as an intern at the Central Intelligence Agency. Although he has no formal journalistic education, he opted to pursue a career in journalism rather than stay with the agency after school, having been a self-proclaimed "news junkie" since he was "in utero."