Cousin, who has been tracked by Rangers since the disintegration of his relationship with the Lens supporters, passed a medical and signed a three-year deal ahead of last night's deadline for the Champions League third qualifying round.
"I'm very happy to be a player for Rangers," said Cousin, who could be part of the squad for tomorrow's Clydesdale Bank Premier League match with St Mirren.
"I'm really glad to play with this club. It's an historic club, and I feel very happy and very proud. I am not 100% fit, but if the coach asks me to play this weekend then I will play.
"I saw Ibrox earlier today and it is a fantastic stadium. I cannot wait to play there for the first time."
Gers boss Walter Smith said: "I am obviously happy to get this deal done and we look forward to seeing Daniel play for Rangers.
"He is a very powerful striker and will bring something different to the squad. He's nowhere near as tall as the 6ft 7ins reported in some places, but has a great presence and is also good on the ground."
Smith added: "Like Jean-Claude Darcheville, Daniel is a player who wants to try something different and this is a chance for him to do that. He is very experienced and is mature enough to cope with such a change."