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Jónsson made his debut as a 15 year old for Fjarðabyggð in Iceland. After that he trained with Þór Akureyri. In July 2005 he signed for Hearts and has been there since. He signed pro contract soon after he turned 18. Then Jonsson made his debut for Hearts on the 20 September 2006, appearing as a substitute in a 4-0 League Cup victory over Alloa Athletic. He made his home debut as a substitute in Hearts 1-0 win over Inverness Caledonian Thistle F.C.