The Library of the Hungarian Academy of Sciences was established by historian Count József Teleki, the first President of the Academy, who offered his 30,000 volume library to the Academy in 1826.

Count József Teleki
The Library began operation in 1831, simultaneously with the Academy itself. The collection, growing with help from various sources, was opened in 1844 for scholars after the necessary organizing and processing work had been completed. In 1865 the Library received suitable and up-to-date accommodation in the newly constructed palace of the Academy, built to the plans of August Stüler. These favorable conditions made it possible in 1867, in accordance with the intention of the founder, for the Library to be opened "for the use of all citizens of the country".

In the course of the following decades the collection was developed from several sources like valuable endowments, legal deposit, exchange contacts with foreign learned societies and academies, by purchasing foreign books and subscribing to foreign periodicals. The main fields of interest were first defined in 1869 while Baron József Eötvös headed the Ministry of Religious Affairs and Culture.

The steady development of the Library came to an end with World War I. The investment capital of the Academy lost value due to inflation, publishing activity was almost completely given up. The majority of exchange contacts was interrupted as a result of the diminishing number of exchangeable publications. The lack of funds and the war psychosis had a bad influence on collection development which could hardly be compensated for by the Vigyázó bequest acquired by the Academy in 1929. Between the world wars, the development of the Library stagnated and, in spite of all efforts, it could not sustain its former standard. World War II caused only minimal damage to the building and after the restoration the institution could function again. The reorganization of the Academy in 1949 represented a landmark in the history of the Library.

The Hungarian Academy of Sciences became the supreme learned body of the country; accordingly the mission of the Library was redefined, to support the research work carried out in the institutions of the Academy. The rapidly growing holdings of the Library involved storage problems immediately after the reorganization. The only solution to this was an independent library building. After several aborted plans it was decided to convert the one-time tenement house of the Academy at no. 1. Arany János Street (originally built between 1863–1864) to library use. The special collections of the Library remained in the headquarters of the Academy. The new Library was opened to the public in November 1988.

János Arany
Act XL (1994) on the Hungarian Academy of Sciences as well as paragraph no. 75 of the Academy's Statutes define the scope of the Library's activities:

The Library of the Hungarian Academy of Sciences disseminates knowledge and promotes scientific research. Historically, it is a national institution making available traditional (printed, manuscript and archival) holdings as well as other information media.

According to paragraph no. 63 of Act CXL (1997) on the protection of cultural property and museum-type institutions, the provision of public library services and culture, the Library is a special national research library.

The Library of the Hungarian Academy of Sciences is a founding member of the Hungarian Shared Cataloging Project (MOKKA). As a participant in the National Document Supply System (ODR), the Library, drawing upon its unique holdings, handles a substantial portion of interlibrary loans in Hungary.

In 2001 the Library of the Hungarian Academy of Sciences celebrated its 175th anniversary with the staging of a memorial session, an exhibition, the release of a festive volume as well as by laying a commemorative plaque at the tomb of its founder.