The 20-year old Iceland U21 international has penned a pre-contract agreement with the Hoops and will officially commence his four-year deal from homeland club Fram in January.
"I'm really delighted to sign for such a big club like Celtic," he said. "This is just a dream come true for me.
"And playing for a big club like Celtic will certainly increase my chances of playing for the national side and hopefully I can break into the squad ahead of the Euro 2016 qualifiers."
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