Ögmundur made his senior debut for Fram on 12 June 2006, a week before his 17th birthday, in the 2006 season of the Icelandic second tier, starting against Haukar in the absence of Gunnar Sigurðsson.
[11] On 16 July 2014, half-way through the Icelandic 2014 season, Ögmundur joined Danish club Randers, signing a one-year contract.
Ögmundur replaced Johannes Hopf as Hammarby's first choice goalkeeper halfway through the season, after the latter chose to make a move abroad.
[24] On 7 July 2020, Kristinsson signed a three years' contract with Greek Super League club Olympiacos for a transfer fee of €400,000 from AEL.
[25] On 5 July 2024, News started to spread that Kristinsson signed a three years' contract with Icelandic giants Valur on a free transfer from Greek second division club A.E.
Despite putting on a solid effort, Iceland went on to lose with the score of 1–0 after a free kick goal by Selçuk İnan in the 89th minute.
[29] Played on China Cup 2017, where Iceland won silver medals[30][31] Ögmundur has a bachelor of law and has stated that he wishes to become a lawyer after his football career.