The 23-year-old has undergone a medical and held talks at Celtic Park yesterday.
"I have taken the medical, maybe tomorrow it's all going to be figured out," said Johansen, who was part of the Stromsgodset side that won the Norwegian league last year. The midfielder revealed he had spoken to his compatriot Tom Rogne, the Celtic defender, about his imminent switch to Glasgow.
"I talked a little bit with Thomas because I played in the [Norway] under-21s with him," he said.
"I have heard from the national [team] guys that it's a fantastic city and the Celtic fans are unbelievable. I hope it's going to work out and I'm looking forward to it."
Meanwhile, Celtic have loaned Paul George, the 19-year-old midfielder, to SPFL Championship title challengers Hamilton until the end of the season, but Tom Rogic's loan move to Vegalta Sendai is in doubt after it emerged the plamaker would only be able to feature nine times for the club.