BHA was founded in 1947 by a group of preservationists and historians, including prominent citizen J.T. Canales. BHA opened Brownsville's first history museum at Fort Brown. While there, BHA acquired a vast collection of photographs, artifacts and documents. In 1958, BHA acquired the Stillman House through a donation from Chauncey Stillman. BHA then donated the house and all other facilities to the City of Brownsville. In 1960, BHA opened the Stillman House as a public museum and moved its operations to this location. In an effort to keep pace with institutional changes and collections growth, BHA added the Heritage Resource Center in 1988 as a storage facility for its archival collections. It later added an interpretive photographic museum called the Brownsville Heritage Museum in 2002. Aiken Education Center was added in 2004 to provide much needed additional programming space and a gallery for rotating temporary exhibits. Together, this group of facilities is known as the Brownsville Heritage Complex.

As part of its strategic plan, BHA increased its cemetery preservation program and opened Old City Cemetery Center in October 2007. As a part of this project, BHA also partnered with the City of Brownsville in 2007. This partnership was awarded the Preserve America Designation and a grant to promote and enhance the heritage of Brownsville while attracting visitors to the region. In that year, BHA also entered into a contract with the City of Brownsville to restore and turn Market Square into a Heritage Tourism site. The Market Square plans include museums, a research center, and art space. Market Square will showcase significant Mexican Art from Mexico City known as the Backal Collections, of which BHA is the steward. The Backal collection includes Spanish Colonial Silver, 15thcentury Illuminated Manuscripts, Retablos, Mexican Calendar paintings, as well as works by Mexican masters such as Miguel Covarrubias, David Alfaro Siqueiros, and Carlos Orozco Romero and others. With collections moving to Market Square, BHA changed the Heritage Resource Center into the Preservation Research Center, which opened in May 2009.

In 2009, BHA also opened the Southmost Heritage Center in partnership with the City of Brownsville Parks and Recreation Department. This center serves the Southmost community, especially the youth, in order to provide a valuable and unprecedented outreach service to the Southmost area.

Along with preserving important historical and cultural landmarks, BHA provides year-round programming in these venues. These programs seek to connect the people of Brownsville with the cultural traditions that pass from one generation to another and share the richness of our cultural diversity. Programs range from fine arts exhibits, popular cultural events, musical performances, school collaborations, literary publications, community pride celebrations, and preservation workshops. BHA provides venues for established and emerging artists, historians, preservationists, performers, local residents and tourists to engage in cultural activities designed to enrich and inspire. BHA works with a wide range of community partners and volunteers to provide community-based heritage and cultural arts programming, with admission to 90% of its programs offered free of charge to the community. It is BHA's organizational belief that no one should be deprived of cultural experiences because of socio-economic circumstances.