The former Nottingham Forest coach is back in the Premier League after losing his job midway through last season.
Cooper felt that he was not treated fairly by Forest and will hope to get more backing at Leicester.
“I’m really excited, it’s a brilliant challenge,” said Cooper, speaking to his new club.
“It’s something I really can’t wait to get going with. I’m absolutely motivated for my next challenge, which I’m lucky enough to say is at Leicester City.
“My next chapter was one that I knew had to be right and in my gut I really needed to feel was the right thing and this feels all of those things to me. In the end, it’s about the job that you do, how the teams plays, the results that you get and the way that you go about it.
“That is the nature of the game and our game. Of course, you want to do it in a certain way and you want to do it within what a club stands for. It’s the same for any manager. For me, that’s my challenge here now and I’m so committed to show the best of me for this football club, hoping that we can have some success together.
“I’m in a personal position where I’m really hungry and motivated and I’m just really glad that I’ve got this challenge. My next challenge is going to be a really important one and to get it at a club like this is something that I can’t wait to get going with.”