The Scottish champions have confirmed that the Iceland Under-21 international will be moving to the club on January 1 and has signed a four-year contract
The 20-year-old striker, scorer of 14 goals in 50 appearances for the Icelandic club, 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 revealed last week that a fee had been agreed between the two parties, and the Bhoys confirmed on Wednesday that 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," Fridjonsson told Celtic's official website.
"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.