The New Zealand international moved to the City Ground during the January transfer window, where the Magpies inserted an obligation to buy clause into the agreement.
It’s understood the £15million clause was triggered in February when Wood started his third game for Forest, which ended in a 2-0 defeat at Fulham.
The 31-year-old had featured in all but one of Newcastle’s matches before his departure. United head coach Eddie Howe did plan to lose Wood but respected the striker’s wishes.
Wood’s exit left Howe short in attack but he managed to get by after Callum Wilson and Alexander Isak stayed injury free to help seal a Premier League top four finish.
“He’s been a huge player for us, outstanding in every way,” Howe said on Wood. “When we signed him, we were in a very difficult league position. He played a huge part on the pitch to help transform the team.
“He’s been excellent, both on and off the pitch, in terms of his leadership and positivity even when he’s not played. You can’t underestimate the role he’s played.
“It was a difficult decision because you have to take into account the player and his wishes. But also, I think it’s a very good deal financially for the football club.”
Speaking about his decision to move to Forest, Wood said: “It’s good, it’s different, it’s a change.