The 26-year-old joined the Centurions from boyhood club Hull KR ahead of the 2017 campaign but only made nine appearances as Leigh dropped out of Super League.
“I’m absolutely over the moon to be signing for the Tigers,” said Green.
“When you get relegated with one club you don’t expect the League Leaders’ (Shield winners) to come calling just a few weeks later. The move came about virtually overnight.
“My agent rang me saying Daryl (Powell) wanted to talk about me joining the club and within around three or four hours the deal was all signed and I had joined the Tigers.”
Green is Castleford’s fifth recruit for 2018 following the additions of fellow prop Mitch Clark, winger Garry Lo, centre Joe Wardle and half-back Jamie Ellis.
“I’m delighted that James has agreed to join us for next season,” said Powell. “He is a big aggressive running front-rower who will add to our already strong pack options.”