The 23-year-old lock began his career with Leicester Tigers before moving to Leeds in 2012.
"Calum has already shown he is more than capable of performing in the Aviva Premiership during his time with Leicester, and I'm delighted he has made the decision to move to Newcastle," director of rugby Dean Richards told the club's official website.
"His strong displays for Leeds over the last two seasons have really caught our eye and he is at a good age with an amazing amount of potential. He is a fantastic signing."
Green won eight caps for the England Under-20s between 2009 and 2010.