The Wolverhampton born defender has only played for Leicester City during his career, making 116 appearances and scoring 7 goals.
Wolves have signed Richard on a 4 year deal for a undisclosed fee
Leicester's Chief Executive Lee Hoos told Leicester's official website: "Richard is an emerging talent who we were keen to hold on to and help us in our quest to gain promotion from League One.
"However, his representatives made it clear to the Chairman that they were not interested in discussing new terms due to our League One status, which is very frustrating for us.
"There is no way we could allow a contract to expire and face the prospect of a tribunal, so it was in the best interests of the club to secure the deal with Wolves."
Chairman Milan Mandaric added: "Richard has been a loyal servant to Leicester City for over 10 years and we wish him well.
"If we had stayed up, I think we could have agreed a new contract with the player, but unfortunately this was not to be.
"However, I can assure our fans that our new manager Nigel Pearson is fully focused on strengthening the squad and has already identified several targets, who he'd like to bring to the club before the start of the season."