Blount Hall was built as an addition to the George C. Taylor Law Building, being connected to the older building by a 12-foot-high, glass-walled-interior walkway. It was completed in 1971. The building was constructed with state money and a $200,000 federal grant. It was designed to add 54,000 square feet to the College of Law facilities—a large part of which was to accommodate the Law Library. The third floor of the building is a library stack floor with structural stacks and a low ceiling. The addition was separated from the Law Complex during the renovation and expansion begun in 1994 and completed in 1997. Following completion of the Law Complex, the building was first used to house the Division of Continuing Education, which moved from the Communications Building. With the relocation of those functions to the Conference Center Building, the building was devoted primarily to Research Office functions.
The architect for the building was David Liberman, who characterized the design of the building as contemporary. Following the separation from the Law Complex, the building was called the White Avenue Building. This designation became confusing when a White Avenue Biology Annex was constructed a block away, and in 2010 the names of both buildings were changed. The White Avenue Building became Blount Hall, preserving the original name of the institution and recalling the enrollment of Barbara Blount. The White Avenue Biology Annex became Senter Hall.