Education
He started his career with local team Kansas in Siglufjörður and later played for ÍA Akranes, winning the Icelandic league in 2001, before going abroad to play professionally for Swiss club Bachelor of Science Young Boys.
He started his career with local team Kansas in Siglufjörður and later played for ÍA Akranes, winning the Icelandic league in 2001, before going abroad to play professionally for Swiss club Bachelor of Science Young Boys.
In 2005, Grétar signed for Arizona Alkmaar as a replacement for January Kromkamp. On 2 July 2007, Arizona Alkmaar announced they had accepted a €3.5 million bid from Middlesbrough. Gareth Southgate had seen him as an ideal replacement for Stuart Parnaby.
After the bid was accepted, however, Arizona backtracked, claiming the price wasn"t high enough and requested Middlesbrough to raise their bid to £4m.
Instead, Middlesbrough turned their attention to Charlton Athletic right back Luke Young, who ended up making the move, ending Middlesbrough"s interest in Grétar. Despite signing a new four-and-a-half-year contract with Arizona in November 2007, Grétar signed for Bolton Wanderers on 16 January 2008 for a £3.5m fee.
He made his debut against Newcastle United on 19 January 2008. He scored his first goal for Bolton in the 3–1 victory over Stoke City on 16 August 2008.
In the last but one game of the season, Grétar"s goal in a 1–1 draw against Hull City confirmed Bolton"s Premier League survival.
At the start of the 2010-2011 season, Grétar changed his squad number from 15 to 2. At the end of the 2011-2012 season Bolton were relegated and the club elected not to offer Steinsson a new contract. On 22 August 2012, Grétar signed a two-year contract with Turkish Süper Lig club Kayserispor.
On 27 September 2013 Grétar announced that he had retired from football.
He helped former club Bolton sign Yannick Bastos in 2014. He also played regularly for the Iceland national football team
He made his debut in a March 2002 friendly match against Brazil as a substitute and scored after being only 17 minutes on the pitch. He also represented Iceland at all youth levels.