In 2010 – competing at a World Cup for only the second time following their 1982 debut – New Zealand drew with Italy, Slovakia and Paraguay but failed to reach the knockout stages.
They will face Belgium, Egypt and Iran in the group stage of the 2026 tournament, which is being co-hosted by the US, Canada and Mexico from 11 June to 19 July.
New Zealand will play England in a friendly in Tampa, Florida, on 6 June, three days after facing Haiti.
Wood, who returned in April after six months out with a knee problem that required surgery, will captain the 26-man squad.