The DuSable Museum was chartered on February 16, 1961. Its origins as the Ebony Museum of Negro History and Art began in the work of Margaret and Charles Burroughs to correct the perceived omission of black history and culture in the education establishment. The museum was originally located on the ground floor of the Burroughs' home at 3806 S. Michigan Avenue. In 1968, the museum was renamed for Jean Baptiste Point du Sable, a Haitian fur trader and the first non-Native-American permanent settler in Chicago. During the 1960s, the museum and the , which was located across the street, founded in 1941 by Taylor-Burroughs and dedicated by Eleanor Roosevelt, formed an African American cultural corridor. This original museum site had previously been a social club  and boarding house for African American railroad workers and is now listed as a Chicago Landmark and on the National Register of Historic Places.
The DuSable Museum quickly filled a void caused by limited cultural resources then available to African Americans in Chicago. It became an educational resource for African American history and culture and a focal point in Chicago for black social activism. The museum has hosted political fundraisers, community festivals, and various events serving the black community. The museum's model has been emulated in numerous other cities around the country, including Boston, Los Angeles, and Philadelphia.
In 1973, the Chicago Park District donated the usage of a park administration building in Washington Park as the site for the museum. The current location once served as a lockup facility for the Chicago Police Department. In 1993, the museum expanded with the addition of a new wing named in honor of the late Mayor Harold Washington, the first African-American mayor of Chicago. In 2004, the original building became a contributing building to the Washington Park United States Registered Historic District which is a National Register of Historic Places listing.
The DuSable Museum is the oldest and before the founding of the National Museum of African American History and Culture in the 21st century, the largest caretaker of African American culture in the United States. Over its long history, it has expanded as necessary to reflect the increased interest in black culture. This willingness to adapt has allowed it to survive while other museums faltered due to a weakening economy and decreased public support. The museum was the eighth one located on Park District land. Although it focuses on exhibiting African American culture, it is one of several Chicago museums that celebrates Chicago's ethnic and cultural heritage.
Antoinette Wright, director of the DuSable Museum, has said that African American art has grown out of a need for the culture to preserve its history orally and in art due to historical obstacles to other forms of documentation. She also believes that the museum serves as a motivational tool for members of a culture that has experienced extensive negativity. In the 1980s, African American museums such as the DuSable endured the controversy of whether negative aspects of the cultural history should be memorialized. In the 1990s, the African American genre of museum began to flourish despite financial difficulties. In 2016, the museum formed an affiliation with the Smithsonian Institution.