The 20-year-old has signed a four-year contract and will join up with Celtic on January 1.
Fridjonsson impressed Celtic boss Neil Lennon during trials at the club.
“I’m really delighted to sign for such a big club like Celtic,” Fridjonsson said. “This is just a dream come true for me.
“It is unbelievable to be here and I can’t wait to get started. I was buzzing when I heard of their interest and when Celtic came in for me there was nothing for me to decide. It was just Celtic.
“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.”
Fram chairman Sverrir Einarsson said: “This is a very good piece of business for Celtic and it is very good business for us.”
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.