Rangers wrapped up a season-long loan deal for the Paris Saint-Germain winger on deadline day after a move to Schalke was unable to be completed in time.
In addition to Schalke, Rothen had also attracted interest from Blackburn and he visited the Premier League club earlier in the summer.
However, the France international has revealed he is excited by the chance to play for a club of Rangers' stature and is looking forward to playing in the Champions League.
"I am absolutely delighted to be joining Rangers, a massive club with a great history," Rothen told the club's official website on Tuesday.
"It has been a very busy day, but I have been very impressed with everything and now look forward to a new chapter in my life.
"I did have other offers from Schalke and Blackburn, but I just felt that Rangers offered something different.
"Obviously Blackburn came in first before Rangers. They don't really have the same ambitions as a club.
"Here, I have the chance to win awards, to win titles.
"Playing in the Champions League is, of course, great for the club but there is also a big chance to win trophies in Scotland. This is important for any footballer."