Finnarsson began his footballing career in 2003 at the youth academy of Scandinavian FC. He developed quickly, and was promoted to the main squad in 2004. From 2006 onwards, he became a regular player in the starting eleven and an important player for the team, noted for his leadership and versatility. In 2008 he was also made the captain. He remained at Scandinavian FC until mid-2013, when, reputedly after a dispute with the club's management, he was sold to Quartz Forest FC. At Quartz Forest FC, Finnarsson was immediately appointed captain. He performed well and scored quite proficiently, and at the end of the 2014 season he returned to the First Division when he was bought by FC Harbour, where he was again immediately appointed captain.
Since 2007, Finnarsson has played for the Southern Arc Islands national football team, though he has been called up somewhat irregularly.
Finnarsson is of mixed Scandinavian and Slavic descent.
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