The Icelandic striker, 20, has agreed a four-year deal and officially joins the Scottish champions on January 1.
Fridjonsson, who currently plays for Fram in his homeland, will be unveiled to the media at a press conference at Celtic Park at lunchtime on Wednesday.
He told the club's official website: "I'm really delighted to sign for such a big club like Celtic and it's just a dream come true.
"It's unbelievable to be here, I can't wait to get started."
Speaking after the club's AGM on Friday, boss Neil Lennon said: "He is one for the present. The season is just finished in Iceland so he may need a little bit of a break so we may not see him immediately but I'd like to think he would be making inroads around Christmas time.
"He is a good player for his age, a good size, we had him in for a week's trial and were hugely impressed by him.
"It is not a huge outlay but we think he is a player who will get better and, at 20, he has very good potential.
"Technically he is very good, he is excellent in the air, he leads the line very well and, for the Scottish game, he likes the physical side of thing as well."