The 23-year-old midfielder has penned a three-and-a-half-year deal at Celtic Park, and comes to Scotland having helped the Norwegian side win their first league title in 43 years
The 23-year-old midfielder joins the Scottish champions on a three-and-a-half-year deal, having spent three years at the Marienlyst Stadion.
During his time at Stromsgodset, Johansen helped the club to their first league title in 43 years, scoring four times in 27 league appearances.
He becomes the fourth Norwegian to join Celtic, after Harald Brattbakk, Vidar Riseth and Thomas Rogne, and could make his debut against Motherwell on Saturday.
Johansen explained his Norway team-mates played an important role in his decision to move to the club.
"I talked with some of the guys in the national team and they all said that Glasgow is fantastic, the fans are unbelievable and the club is one of the biggest in the world so it was a pretty easy choice," he told Celtic's official website.
"When you're young, you just dream about something like this happening. The club is so big so it's an unbelievable feeling to be here."
Neil Lennon's men are unbeaten in the top flight this season and sit 10 points clear at the top of the Scottish Premiership with two games in hand on nearest rivals Aberdeen.
Johansen has six international caps to his name and will be unveiled at Celtic Park on Wednesday.