The 25-year-old Australian has made 14 appearances for the relegated Exiles this season following a move from Brumbies in summer 2014.
McCaffrey has represented his country at Under-20 level, but he is yet to receive a call-up for the senior side.
"He is an athletic, ball-playing back-rower with the ability to play in a few positions," director of rugby Richard Cockerill told Leicester's official website. "He's had some experience of the English club game this season and we think there is more to come from him in this environment."
Leicester return to Aviva Premiership action on Saturday when they face Wasps at the Ricoh Arena.