He was Minister for Economic Affairs in the coalition government of Jóhanna Sigurðardóttir.

[1][2] He served as Minister of Business Affairs from 1 February 2009 until 1 October the same year and then served as Minister of Economic Affairs until 2 September 2010.

Gylfi graduated from the University of Iceland in 1990, and received his doctorate from Yale in 1997.

While at Yale, he was a core member of the champion intramural soccer team, The Handsome Lads.

When he received his doctorate, he was already a researcher at the Institute of Economic Studies of the University of Iceland: he joined the Faculty of Economics and Business Administration as an adjunct professor in 1997, and was promoted to associate professor in 1998 and full profesor in 2020.