In 1881 the library moved into the new house of parliament, Alþingishús, and in 1886 the first Icelandic print law establishing the library as a legal deposit library was passed by the Alþingi.
While a lot of debate surrounded the building of Þjóðarbókhlaðan at the time, it resulted in vastly improved consultation, study and research facilities for researchers, university students and the general public in Iceland.