The 20-year-old, who has scored 12 times in 23 games for his club Fram this season, impressed Celtic boss Neil Lennon on two recent trial periods with the champions.
The 6f 3in Iceland U21 international is keen to complete the deal and is hopeful his agent can agree personal terms in the near future.
"It makes me happy to be told Celtic have reached an agreement with my club," Fridjonsson told the Daily Record.
"My trials went well in Scotland and Holland but there was a special feeling around the people in Scotland.
"Everyone at the Celtic training ground and everyone at the club was very warm with me. They made me feel very welcome.
"Now my agent and I must wait to see what Celtic put together."
Earlier in the day Fram chairman Sverrir Einarsson said: "This is a very good piece of business for Celtic and it is very good business for us."