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 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."