The veteran New Zealand international is among the league's top scorers and Forest enter the weekend in third place.
"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," the 33-year-old Wood said in the team's announcement on Thursday.
Wood joined Forest on loan from Newcastle in January 2023 and the deal became permanent at the end of the season.
Wood has scored 14 goals so far this season - tied with Chelsea's Cole Palmer for fourth-most in the league. That tally also matches his career high in the Premier League, with 16 league games still to play.
"I'm excited for the future. This club has a lot of potential to continue to grow and build, and that is what I want to be a part of," he said.
Forest owner Evangelos Marinakis added: "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."
Forest play at Bournemouth on Saturday.
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