ANUBiH members are chosen among the most eminent persons actively engaged in different fields of sciences and arts. They are elected by the ANUBiH Assembly in compliance with the provisions of the Law and Bylaw, pursuant to proposals submitted by those authorized to do so by the Bylaw: departments and scientific units of ANUBiH, two ANUBiH members, and the scientific and artistic institutions of BIH (universities, faculties, higher education establishments, scientific research institutions, academies of arts, and relevant associations in the field of literature and arts).

The active complement of the Academy consists of full members (academicians) and corresponding members of ANUBiH.

In addition, pursuant to the current regulations, the Academy has domestic and foreign members and honorary members. Domestic members are citizens of Bosnia and Herzegovina living outside BIH, while foreign members are foreign citizens.

The Academy's Electoral Assembly elects full and corresponding members by secret ballot, and domestic and foreign members by acclamation.

Honorary members are elected by acclamation at the Academy's Electoral Assembly, on the proposal of the Presidency of ANUBiH and prior statements of departments.

The current active complement of the Academy consists of 48 members: 37 full members and 11 corresponding members of ANUBiH.