The 31-year-old joins Forest on loan, with a conditional offer to join the club permanently until the summer of 2024.
He becomes the club's third signing of the January transfer window following the additions of Danilo and Gustavo Scarpa from Palmeiras, respectively.
"It's a great feeling and I am very thankful to be here," Wood said on the club's official website.
"Nottingham Forest is a massive club which I have come up against a number of times, but it’s nice now to be able to pull on the red shirt and fight for the club.
"You can see the transition over the past 18 months and it’s progressing in the right way. It’s a project that’s going in the right direction."
Forest Sporting Director Filippo Giraldi added: "Chris is a player who has great character and experience, having played 189 games and scored 54 goals in the Premier League."
Wood joins Forest after spending one year at Newcastle in which he scored four goals in 35 appearances. Prior to that he spent five-and-a-half seasons at Burnley in which he netted 49 times in 144 matches.
Forest, in 13th place, are back in action this weekend when they travel to 17th placed AFC Bournemouth, looking to steer further away from the relegation zone.