The Hoops are set to pay £100,000 for the 20-year old in the winter and the player himself is keen to see the contract completed as soon as possible.
"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."
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