Sweden Under-21 midfielder Mervan Celik has signed for Rangers on a three-and-a-half year deal, having passed a medical early on Friday afternoon.
The player had left Gothenburg-based GAIS, who are expected to demand compensation for his development.
Celik will not be available to Rangers manager Ally McCoist to face Aberdeen at Ibrox on Saturday as he has not yet received international clearance.
He told Rangers TV: "I have made it to Glasgow and I am happy to be here."
And Celik, who can play on either wing and began his career as a striker, added: "It has taken some time but it is finished now and I am very happy with that.
"It is a very good set-up here, it is a very nice training ground and everything is perfect.
"I was here last month and the club showed me everything and I liked the set-up so it is good to have the deal agreed now. Of course now I am very hungry to be involved.
"I am a player who always plays with heart.
"It doesn't matter for me where I play, that is for the coaches to decide. Of course the fans can expect to see goals but I can also defend well."
The player, who will wear the number 24 jersey with "Mervan" on the back, was spotted by Rangers scouts Neil Murray and John Brown before leaving GAIS under freedom of contract.
McCoist said: "Neil and John first brought him to our attention and Ian [Durrant], Kenny [McDowall] and I have all had a look and he's very direct and very competitive.
"He can go past people and score goals and he can play wide in a four or five and in one or two games we've seen him through the middle as well.
"He's an all-action player that I think the fans will take to, and more importantly he will be a goal-scoring threat when we get him in the team."
Celik moved to GAIS on a three-year contract in 2009 having started out with city rivals Hacken.
The news of Celik's arrival came hours after Scotland Under-21 attacking midfielder John Fleck completed his switch from Rangers to Blackpool on loan.
Veteran defender David Weir is also to leave Ibrox within days after dropping out of the first-team picture.
Rangers manager Ally McCoist's funds are limited because of debts and an impending tax case.
However, he has this week had 27-year-old Estonian right-back Enar Jaager, who has left Norwegians Aalesunds, and 25-year-old midfielder Jorge Claros, presently with Motagua in his native Honduras, on trial.