The house was built in 1945 by Halldór and his wife Auður Sveinsdóttir. The architect was Ágúst Pálsson and the interior designer was Birta Fróðadóttir. Gljúfrasteinn is built on the banks of the river Kaldakvísl and is situated close to Laxness's childhood home, Laxnes.
Halldór Laxness was a prominent figure in Icelandic society and his status only increased after he won the Nobel Prize in 1955. Laxness's home became a cultural hub in Iceland where important foreign guests were brought for official as well as unofficial visits. International musicians would frequently give concerts in his living room.
In 2002, Laxness's widow, Auður, sold the house to the Icelandic state. In September 2004, it was opened for the public as a museum. Visitors can take a guided tour through the house, and the museum hosts concerts during the summer.