Before embarking on his extensive career in coaching, Teitur enjoyed a successful playing career as a striker for nearly two decades. He signed his first professional contract when he joined hometown club Íþróttabandalag Akraness in 1969. He went on to score 51 goals in 99 appearances for ÍA, with the striker claiming four Icelandic championship titles with the club between 1969 and 1977.
He then made an influential move to French soccer when he joined Lens in 1981. It was at the northern French club that Teitur scored 19 goals during the 1981–82 Ligue 1 season, with the striker finishing fourth in the French top-flight's goalscoring charts. It was also at Lens that Teitur played for former Liverpool, Lyon, and France manager Gérard Houllier before he experienced the tutelage of another top coach in Arsène Wenger at Cannes. In the early 1980s, the current manager of English Premier League giants Arsenal was an assistant coach at Cannes.
In 1988 he landed his first head-coaching role in Norway's top-flight Tippeligaen when he joined Brann. He led the Bergen club to the 1988 Norwegian Football Cup Final and spent the following two seasons at Brann before ending his first spell by moving to Lyn for two seasons in 1991. After a season with Norwegian Second Division club Grei, Teitur took charge of Lillestrøm and led them to second- and fourth-placed Tippeligaen finishes in 1994 and 1995 respectively.
The turn of the millennium saw Teitur return to the Norwegian game for a second spell with Brann. He led the club to a second-place finish in the 2000 Tippeligaen season, and spent two more seasons with the Bergen outfit before making a return to another former club, Lyn in 2003. His final two years in Norway saw him coach second division club Ull/Kisa in 2004 and 2005.
With nearly four decades of experience in European football, Thordarson became the Vancouver Whitecaps men team's head coach after signing a two-year deal with the club on 11 December 2007. Thordarson is the sixth head coach in the club's history. He was at the helm when the Whitecaps claimed their second United Soccer League First Division championship in three seasons after a 2–1 victory over Puerto Rico Islanders on 12 October 2008. The following season Thordarson made several key changes to the Vancouver squad, by releasing many veterans and opting to sign mainly young and experienced players to the roster. Though the Whitecaps struggled in the later part of the season, they claimed the league's final playoff berth. In their playoff run he led the defending champions to the finals again, where the Whitecaps would face the Montreal Impact. The match marking the first time in USL history where the final match would consist of two Canadian clubs. Unfortunately the Caps would end up losing the series 6-3 on aggregate. On 30 November 2009 Thordarson signed a one-year contract extension with the club.
On 1 September 2010, the Vancouver Whitecaps FC held a press conference and Thordarson was named as the coach for the Vancouver Whitecaps' first season in Major League Soccer. After producing only one win in three months of action, Thordarson was released from his contract on 30 May 2011 with Whitecaps Director of Operations Tom Soehn stepping in to replace him in the interim.
On 15 January 2012, Cassius Management announced that Teitur would be one of six foreign coaches hired for the new league Bengal Premier League Soccer, with group stages beginning 15 March 2012. Subsequently he was bought by Basarat, under the ownership of Uro Infra Reality India Ltd. for US$210,000 on 30 January 2012. After several delays caused by reasons such as lack of quality venues and government opposition, the idea for the league was finally axed in January of 2013.