The highly-rated Danish winger, 26, has been capped 40 times for his country and arrives with over 200 senior appearances in European football under his belt.
Skov Olsen’s career began in the youth ranks of FC Nordsjælland, featuring in the Danish Superliga alongside Oliver Antman, where he netted over 20 times in 41 appearances.
After amassing 70 appearances in a three-year spell for Bologna in Italy and three very impressive years at Club Brugge, Skov Olsen has struggled to reach the same level in the Bundesliga.
Speaking after becoming the third addition of the January transfer window for Rangers, Skov Olsen said: “I’m very excited. I’m very happy that it’s done and I’m so excited to meet all the players, fans and the rest of the club.
“Rangers are the biggest club in Scotland with a huge history. It has huge traditions and is a very old club.
“When I finally heard that I had the opportunity to come here, I wasn’t in doubt for a second. I want to come here to try help win trophies with the rest of the team, do my best, and have a great time here.”
Head Coach, Danny Rohl, added: “We are really excited to bring Andreas to the club.
“He is a player who has proven himself at the top level and brings experience of performing under pressure both domestically and on the European stage.
“He will provide real quality in the final third of the pitch and arrives hungry for this challenge and excited by the opportunity ahead of him.”