All Blacks assistant coach Steve Hansen confirmed the appeal will be lodged and possibly heard by an International Rugby Board (IRB) panel tomorrow.
The IRB had found Mealamu guilty of headbutting Moody in the All Blacks' 26-16 win at Twickenham last Saturday, but he was spared an eight-week suspension due to his "exemplary disciplinary record" in 82 Tests for the All Blacks.
Hansen, who formed part of Mealamu's defence team during Tuesday night's two-hour hearing, said: "We're defending a guy who's character has been questioned and it shouldn't be.
"He's a one-off special person. He hasn't got a dirty bone in his body. He's not a dirty player, he never has been. This is a case we'll go to the death on."
Hansen revealed Mealamu's ban had affected morale in the All Blacks' camp. "The guys were gutted because he can't play and more importantly they were gutted for Kevvy because of the man he is," he added. "Everyone knows it's not in his nature to do that and everyone knows if Kevvy says he didn't do it, he didn't do it."
Television footage of the incident showed Mealamu grabbing Moody by the jersey and then diving forward, making contact with the back of England captain Moody's head.
The International Rugby Board's citing commissioner John West on Sunday night charged Mealamu with contravening Law 10.4a - "striking with the head" - and IRB judicial officer Lorne Crerar led Tuesday night's hearing in Glasgow, implementing the ban.
It is understood Mealamu's defence team claimed he made contact with Moody with his shoulder, rather than his head.
Should New Zealand's appeal fail, Mealamu will be suspended until 4 December, ruling him out of Saturday's match at Murrayfield as well as the All Blacks' fixtures against Ireland on 21 November and Wales a week later.