Williams comes into the All Black squad for the back-to-back Bledisloe Cup matches as an injury replacement for Conrad Smith.
A medical for his new Japanese club Panasonic and other administrative issues between the club and New Zealand Rugby Union had delayed Williams' addition to the squad.
The first Rugby Championship match is on Saturday between Australia and the All Blacks in Sydney.
All Black head coach Steve Hansen said: "It's what we expected, but we knew it was going to take a bit of time, and we are now all looking forward to preparing for Saturday's challenge."
"We want to express our gratitude to the three parties involved in getting Sonny available for the All Blacks - Sonny's agent Koder Nasser, the NZRU and particularly the Panasonic Wild Knights - for their roles in allowing us to select him," Hansen added.
