The Denmark international, who has previously had spells with Palermo and Roma, has put pen to paper on a four-year contract with les Dogues
The Denmark international has penned a four-year contract with les Dogues and the centre-half is excited by the challenge of trying to prove himself in France.
"Let me first say that I am really happy to join the club," the 24-year-old told his new club's official website.
"I sincerely hope that we can enjoy a good season together and that, at the end of it, everyone will be satisfied with the results.
"I do not forget that Lille did the double two years ago, so we have to help find a way back into Europe, either in the Champions League or Europa League.
"I want to show my very best qualities here and I hope this will be a great experience in my career."
As well as Denmark and Germany, Kjaer has also plied his trade in Italy, having enjoyed spells with Palermo and Roma.