He is the brother of Teitur Thordarson, former manager of Estonia when Ólafur played against them with Iceland in 1996.
Ólafur started his career at IA Akranes before moving abroad to play in the Norwegian League.
After three decent seasons with Fylkir finishing 3rd in 2009, Ólafur decided to step down from the coaching role after the 2011 season after guiding them to a mid-table finish, allegedly due to disagreement with the board over player transfer issues.
Ólafur was quickly picked up after the 2011 season, in October the same year, to coach Víkingur Reykjavik.
Ólafur made his debut for Iceland in 1984 and went on to collect 72 caps, scoring 5 goals.