The shooting guard started just seven of the 60 games that he played in for the Indiana Pacers last year, before moving to his seventh NBA team in eight seasons during the summer.
The 27-year-old told the team's official website: "You've just got to go out there and compete hard every day. I'm all about winning. It doesn't matter if I start, or if I don't start, if I play or if I don't play. As long as we're winning, that's all I care about.
"My main goal is I want to win a ring. I got drafted in 2005. I don't know how many years I have to play. Hopefully I've got another 10 years left. But my main goal is to win an NBA championship.
"Even if I'm the 15th man on the bench, the first man off the bench, or I'm starting, I'm still part of that team. I want to be a part of winning a championship. I feel like this team is going in those right steps, and I'm happy to be part of this team."
Green has a career average of eight points per game.