"There is only one reason for my decision and it is my ambition to manage in England and get into the Premiership," the 40-year-old Scot said.
"It was hard to say goodbye to some good friends and people I enjoyed working with immensely, and particularly the players who gave me the opportunity to join such a fantastic club as Leicester.
"For a year or so now I've been looking, and I realised to get to the English Premiership, where I wanted to be, it would be difficult to do that from a provincial club, which Hearts are.
"I've been looking for a club with the same ambition as I have, and the recent history of Leicester would dictate that they are a Premiership club.
"I'm very confident that we match each other's ambition and we can move forward together."