The House of Parliament was built in 1880 - 1881. It was constructed from hewn blocks of the gray basaltic rock (dolerite) upon which a part of the capital rests. The architect was the Dane F. Meldahl, the director of The Academy of Art in Copenhagen and the Danish mason Bald. The first assembly of the parliament in the new building took place on July 1. 1881.
The National Library, The National Archives and the National Museum were housed there for a while until the museum building was ready. The University was housed there from its establishment in 1911 to 1940, when its main building was ready. The Danish governor's office was there between 1941 and 1944, when the Icelanders proclaimed the republic in the Parliamentary Plains in 1944. The garden behind the building was named after one of the members of Parliament, prime minister and a renowned entrepreneur, Tryggvi Gunnarsson, who lies buried there.