The 39-year-old joins the Aviva Premiership side from Dunedin-based outfit Highlanders.
Thorn won 60 caps for the All Blacks during a successful international career that lasted from 2003 to 2011.
"He is a very driven individual. He wants to play in the Premiership and he wants to win the Premiership," Leicester director of rugby Richard Cockerill told the club's official website.
"He will turn 40 during the season but if anyone questions his age or commitment, you wait until you meet him. He is one of the great all-time rugby players the world has ever seen."
Leicester start the new season on September 6 when they host Newcastle Falcons.