The 20-year-old striker, the scorer of 14 goals in 50 appearances for Fram Reykjavik, has put pen to paper on a four-year deal with the Scottish champions, who are reported to have paid a fee of around £100,000.
Celtic manager Neil Lennon confirmed last week that a fee had been agreed between the two clubs and the youngster has now finalised his transfer, which will see him join officially on January 1.
"I'm really delighted to sign for such a big club like Celtic and it's just a dream come true," said Fridjonsson.
"It's unbelievable to be here, I can't wait to get started."
Fridjonsson has been capped six times for Iceland Under-21s, scoring once.
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