The 34-year-old has been sidelined since October due to a knee injury. He underwent surgery in December.
His return was confirmed by Forest coach Vitor Pereira in a press conference ahead of the club's Europa League quarter-final first leg match against FC Porto on Thursday.
"He's started training with the team and is available for the game," Pereira said on Wednesday.
Wood, who is the All Whites' record goalscorer with 45 goals, played for New Zealand when they last qualified for the World Cup in 2010 in South Africa.
New Zealand are in Group G at the World Cup, where they will face off against Belgium, Egypt and Iran in June.