The BCC was established in 1957 through the efforts of civic-minded groups who felt that there was a growing need for more higher education facilities in the Bronx. Classes began at Hunter College, and later at the former site of the Bronx High School of Science.
In 1973, the Dormitory Authority of the State of New York acquired the University Heights campus from New York University, who had sold the campus under threat of imminent bankruptcy. Beginning in the fall of that year, the BCC moved its operations to the spacious and modern 55 acre (223,000 m²) site overlooking the Harlem River.
In 2001, parts of the motion picture A Beautiful Mind that depicted MIT were instead filmed in the BCC, due to the film's low budget. The dome at BCC was also used in the filming of The Good Shepherd, an upcoming Robert De Niro film.