The veteran centre-forward has penned a new agreement to 2027.
"I'm very excited and very happy to have it completed and done, and I'm looking forward to the next couple of years, at least," Wood, 33, said.
"I saw the ambition when I first arrived. When I spoke to the owner and his family and saw where they want to be and where they see this club to be - it was clear they have high ambitions and big dreams. He has backed the club for years, even before promotion to the Premier League, which is fantastic, and the team is pushing in the right direction.
"I can't thank the fans enough, they always come in voice and they're always behind the team and myself, it's a pleasure playing in front of them. Here's to a few more years together."
Forest owner Evangelos Marinakis also stated: "He has performed exceptionally well with us.
"More than just his goals, he epitomises everything that it means to wear the Garibaldi red - hard work, a fighting and winning spirit, and the attitude to never give up. He is a winner and a role model to inspire all of us, and we reward his dedication with ours."