The 27-year-old right-back has signed a three-year deal with the Foxes, having passed a medical on Saturday.
"I'm really pleased that we have been able to secure a defender of Danny's quality. He will add more good competition to our squad, which is very healthy for the group," manager Nigel Pearson said.
Simpson added: "I'm really excited. I've had a look around the facilities, which look fantastic, and had a good chat with the manager, who I'm really looking forward to working with.
"He told me that there's a good group of players here that demand a lot of each other and I think, from speaking to other people, he knows I'll work hard every day to fit into that. I've got a really good feeling about this."
For the big stories and the banter follow us on Twitter: @tribalfootball