The 27-year-old completed his medical and put pen to paper on a three-year contract at the King Power Stadium on Saturday.
Simpson, who also played for Manchester United and Newcastle United, is the Foxes' second signing in just over 24 hours after the conclusion of a deal to bring veteran midfielder Esteban Cambiasso to the club.
Boss Nigel Pearson said: "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.
"He already knows a number of our players from his time with Manchester United and he is the kind of character we look for, so I'm sure he will settle in quickly."
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.”
Simpson will not be able to play in Sunday's Premier League clash with Arsenal but will be eligible for his Foxes debut after the international break when they travel to Stoke City on September 13.
Watch Leicester's Premier League clash with Arsenal live on Sky Sports 1 HD from 3:30pm on Sunday.
It's a long time since he was supposed to be Gary Neville's successor...- shea666