In April 2005, the Senate of the University of Iceland appointed a committee to work on the preparation of a building designed to house the teaching of foreign languages at the University of Iceland, with a lecture hall/auditorium, exhibition spaces, a library and data storage, offices for the contemporary teachers of the Department of Foreign Languages (now the Department of Languages and Cultures), and facilities for meetings, symposia, study areas for students of foreign languages, and a coffee bar. As a result of the committee’s work, an open competition for the design of the building was held in 2011, and the winning entry was made by Andrúm architects.

The ground was first broken in a ceremony attended by Vigdís Finnbogadóttir, Illugi Gunnarsson, then Minister of Education and Culture, and Kristín Ingólfs­dóttir, then Rector of the University of Iceland, on Women’s International Day, 8 March 2015. A competition was established to find a name for the new building, the winning entry being Veröld – House of Vigdís.   

Veröld – House of Vigdís was officially opened on 20 April 2017, and the Vigdís International Centre for Multilingualism and Intercultural Understanding began operations on the very same day.

There is a special room in Veröld dedicated to Vigdís Finnbogadóttir in which there is an exhibition celebrating her life and work. The Vigdís Square, outside the building, is designed to reflect her experience in the world of theatre, and the planting of a birch tree there commemorates her interest and participation in the preservation of nature, the reclamation of land and reforestation. As of June 2020, Veröld’s main auditorium has been named Auðarsalur (Auður’s Hall) in honour of Auður Hauksdóttur, who was then retiring and who had been the director of the Vigdís Finnbogadóttir Institute for Foreign Languages from 2001–2018.