Árnadóttir obtained a master's degree in public administration and governance from Syracuse University.
On 29 December 2000 by unanimous decision by the four members of the City Council, she was appointed Director of Development and Information from 2001-2005, later continuing her work in the mayor's office.
[2][3] She was given leave in July 2007 to act as project manager of Iceland's bid to join the UN Security Council, which was voted on in October 2008.
[4][5] She was immediately after the UN vote given the position of head manager and ambassador for the newly combined offices of Minister and Secretary of State within the Icelandic Ministry of Foreign Affairs in November 2008.
[7] From 2010 to 2013, she was an ambassador to China (and non resident ambassador to Australia, Cambodia, Laos, Mongolia, New Zealand, North Korea, South Korea, Thailand and Vietnam) The credential confirmation for her ambassadorship to China was conducted on 11 January 2010 by then president Hu Jintao.