The museum's true founding moment came in 1963, when artist and teacher Hans Hofmann donated forty-five paintings and $250,000 to the university. Hofmann, a German-born abstract expressionist who had taught a generation of American painters, was betting that Berkeley could build something worthy of his life's work. A design competition was announced in 1964, and the building conceived by architect Mario Ciampi opened in 1970 - a dramatic Brutalist structure of cascading concrete galleries. Peter Selz, recruited from the Museum of Modern Art in New York, served as founding director from 1965 to 1973, championing unorthodox Bay Area artists and setting a tone of adventurous collecting that the museum has never abandoned. His successor James Elliott directed until 1988 and founded the MATRIX Program for Contemporary Art in 1978, an ongoing series that has introduced emerging artists from around the world.

While the art museum grew in the light, a parallel institution developed in darkened screening rooms. Sheldon Renan began showing films on the UC Berkeley campus in 1966, and was appointed director of the new Pacific Film Archive when it was formally established in 1967. The PFA took a distinctive approach: programming films not as entertainment but in theoretical and critical context, exploring, for instance, film noir through the lens of postwar anxiety. Lectures by scholars and visits from filmmakers added layers of interpretation. Over the decades the archive accumulated 18,000 films and videos. Its collection of Japanese cinema - the largest outside Japan - became a destination for researchers and cinephiles worldwide. The PFA also maintains a library, a study center, and CineFiles, a searchable online database of documents associated with its films.

Some of BAMPFA's most significant acquisitions have arrived not through purchases but through gifts that transformed the museum's identity. In 2009, Fernando Botero donated fifty-six paintings and drawings from his Abu Ghraib series, which the museum has exhibited annually as Art for Human Rights. In 2014, the Steven Leiber collection of Conceptual art and Fluxus materials arrived, prompting the New York Times to declare BAMPFA "one of the world's most important centers for the study of Conceptual art." But the acquisition that may prove most consequential came in 2019: the Eli Leon Collection of nearly 3,000 works by African American quilt makers, including more than 500 by Rosie Lee Tompkins. The quilts now account for roughly fifteen percent of the entire art collection. BAMPFA's 2020 retrospective of Tompkins drew a review from the New York Times calling it "a triumphal retrospective" that "confirms her standing as one of the great American artists - transcending craft, challenging painting and reshaping the canon."

By the 2000s, Mario Ciampi's original Brutalist building was seismically unsafe. Plans for a replacement designed by Japanese architect Toyo Ito were announced in 2008, then cancelled a year later as the economy faltered and fundraising stalled. BAMPFA pivoted. Rather than building from scratch, the museum commissioned Diller Scofidio + Renfro to transform a 1939 Art Deco printing plant at 2155 Center Street in downtown Berkeley - a building on the California Register of Historic Resources, notable for its role in publishing the United Nations Charter. The $100 million renovation wrapped the original concrete shell in a new metal-clad, skylighted addition containing galleries, a 232-seat theater, a store, and a learning center. The museum reopened on January 31, 2016, with 25,000 square feet of gallery space inside an 83,000-square-foot footprint. The vacated Ciampi building, added to the National Register of Historic Places in 2014, was seismically retrofitted and reopened in late 2021 as the Bakar BioEnginuity Hub, an incubator for biotech startups. Both structures survived, repurposed for new centuries.