The Glasgow clubs were drawn to face each other in the competition in what will be their first meeting since Rangers' financial troubles saw them drop down to the fourth tier in 2012.
Johansen, who joined the Hoops from Norwegian club Stromsgodset earlier this year, is quoted by BBC Sport as saying: "We are just happy. We were hoping to get Rangers. It is a great game for us and the fans.
"It is a semi-final and a great game. It would be good to beat Rangers and go through to the final. It is obviously a big game. When I played in Norway, they played it on the Norwegian TV channels.
"When you watched them, you had a feeling about how big they are, but I think you need to take part in the game before you really know how big they are, so I am looking forward to it."
Aberdeen and Dundee United will meet in the other last-four tie.