The former rugby league star was banned for four matches in July after his dangerous tackle on Anthony Watson during the second Test between the All Blacks.
He was sent off during the match and his suspension was set to rule him out of the Bledisloe Cup match on August 19.
The Blues centre is already out of the combined matches against Counties Manukau and Taranaki on August 11 - which consists of 40 minutes against Manukau before a second-half against Taranaki.
World Rugby had originally branded the games 'not meaningful' but Williams' appeal has now been accepted and he is set to play a full role in their Rugby Championship campaign.
A World Rugby statement read: "A game being played by New Zealand against Counties Manukau and Taranaki on August 11 that had been excluded from the suspension by the original disciplinary committee has now been deemed to comply with the regulations' definition of a "match" and, as such, that match will be included as part of the player's suspension.
"Accordingly, Williams is suspended from all forms of rugby up to and including 11 August."