Love Rugby League first broke the news of Green’s switch several weeks ago.
Green has signed a two-year contract from 2017.
The 25-year-old forward was offered a new long-term deal by the Robins earlier this season but decided his future lay away from the Lightstream Stadium.
A shoulder injury eventually curtailed Green’s final season with the club, but he leaves for pastures new having made 82 first team appearances for Rovers since making his competitive debut in 2012.
HUll KR Head of Rugby Jamie Peacock said: “We have known about James’ decision for some time now and it is no way linked to Saturday’s result.
“We have simply held off making any announcements until the end of the season so that we could focus on matters on the field.
“Whilst it is disappointing that he won’t be staying at the club, we offered him a new long-term contract at a level that we felt was fair within our squad.
“From his point of view, he has been given an opportunity to join Leigh and we understand his reasons for moving on. A player’s career is too short to have any regrets and he leaves with our best wishes for the future.
“We had already identified and secured an experienced replacement for James for next season and we’ll now renew those conversations as we look to assemble a strong squad to play in the Championship in 2017.”