Johansen, who has played for Norway at every level from under-16 to full squad, had been courted by several clubs but has opted to speak to Celtic. He should be the first signing of the transfer window for the Scottish champions, who are also trying to enlist a striker.
Johansen flew from Norway's international training camp last night to negotiate his transfer from Stromsgodset, the club he joined from Bodo/Glimt in 2011.
An attacking midfielder, dubbed the Norwegian Modric, Johansen has six caps and has scored once in six international appearances.
He will strengthen Celtic's midfield options as Joe Ledley, the Welsh internationalist, ponders his future and Tom Rogic, the Australian internationalist, prepares to head to the J-League in Japan on loan to Vegalta Sendai to enhance his prospects for Australia's campaign for the World Cup in Brazil in June.
Ledley and Georgios Samaras, the Greek forward, are both out of contract in the summer and Celtic will continue talks with representatives of both players today.
Ronny Delia, manager of Stromsgodset, said: "There has been much speculation about Stefan, but it seems that now he will get his move and it is much deserved. He has been given permission to talk to Celtic and I am proud that I have been allowed to work and develop a player such as Stefan. He's the first player we've had at Stromsgodset who has been good enough to get to the level of the national team. Stefan has taken football at this club to a new dimension and he has kept improving."
He also outlined the capabilities the midfielder would bring to Celtic.
"He has an intensity in his defensive work from midfield, which is great. He is very calm with the ball and has a vision that very few others have. Stefan also has been blessed with a natural passing game and was a creative factor in our team. He is also a winner."
Johansen's agent said the player had been approached by several clubs, including one in Serie A, and Delia added: "He would have been a success in Italy, too, I have no doubt about that."
Jan Aage Fjortoft, the former Norwegian internationalist who played for Swindon Town, Barnsley and Middlesbrough, said Johansen was one of his nation's leading prospects. "In Germany they talk about the No.6, the No.10 and the No.8. He is a No.8 . He is a little in-between. He is a modern midfielder."
Johansen's contract with Stromsgodset runs out at the end of the year so the club are keen to secure a transfer fee for him before free agency kicks in.
Neil Lennon and his squad travelled back to Glasgow last night after losing in a penalty shoot-out to Galatasaray in the Antalya Cup with the Celtic manager keen to add to his squad with a striker the priority despite the improved form of Teemu Pukki and Amido Balde in Turkey.