The 23-year-old arrived in Glasgow on Monday night and is expected to undergo a medical on Tuesday.
Johansen was part of the Stromsgodset side which won the Norwegian league last year but he views a move to Parkhead as a major step forward in his career.
He told reporters at Glasgow Airport: "Hopefully everything will go to plan and I can become a Celtic player.
"I'm having a medical and I'll be really happy if everything works out.
"It's a very big club. Obviously, Champions League, they are leading the Scottish Premiership...so it is a big attraction."