The 24-year-old centre-back, who has also spent time at Palermo and Roma in Italy, has revealed his delight at signing for the 2011 champions of France.
"They have a great stadium and the best training ground I have ever seen," wrote Kjaer on Twitter.
"I have had a few days in Lille before finally signing. I'm so impressed by a well-organized club and my boss Rene Girard.
"Lille was the first club I visited to train with as a teenager - even before Real Madrid. My first love."