The trio missed the July tests against Fiji and Tonga, but have been included in coach Ian Foster's 36-man squad for the upcoming tournament.
Prop George Bower will remain with the squad as injury cover for Moody, who is not expected to return to Test rugby until after the Bledisloe Cup Series.
Hooker Samisoni Taukei'aho will also stay with the All Blacks squad as cover for Asafo Aumua who missed the two tests against Fiji. Aumua may also play the opening round of the NPC to build his match fitness.
69-Test halfback Perenara recently returned from Japan and has been playing club rugby for Norths in Porirua.
He will also play NPC rugby. New All Black Finlay Christie will remain as temporary cover with the squad.
Midfielder Braydon Ennor, who missed the July tests to undergo appendicitis surgery, has been named.
125-Test lock Sam Whitelock will again captain the All Blacks, in the absence of Sam Cane who is still recovering from chest surgery. As well as Cane, midfielder Jack Goodhue was also not considered for selection due to injury.
All Blacks Head Coach Ian Foster said: "It's exciting to be naming the squad for the Rugby Championship and we can't wait for the next phase of our Test season.
"The July series gave us a great opportunity to grow some depth and experience. It also enabled us to re-establish some returning players, both from overseas or from injury. The Bledisloe Cup plus the Rugby Championship are pinnacle challenges for us and remain as our top priorities. There is real excitement in the group for these opportunities in front of us," he added.
The All Blacks will have a two-day camp in Christchurch next week before assembling in Auckland for the pre-Rugby Championship Bledisloe Cup Test presented at Eden Park on Saturday 7 August. The second Bledisloe Test is at Optus Stadium, Perth, on Saturday 21 August, with the third back home at Sky Stadium, Wellington, the following Saturday, 28 August.
"Our players are looking forward to spending some time at home before what is shaping up to be a hugely-competitive Rugby Championship. The Bledisloe Cup Series is a great way for us to kick off this part of the season," Foster said.
"It's our first challenge; we're playing for a trophy that is massively important to us, and we're both coming in fresh off our respective Series wins, so it bodes well for a great Series."
Following the Bledisloe Cup Series, the All Blacks will then play four Tests in a row in September, with back-to-back Tests against Argentina, at Eden Park on Saturday 11 September and Sky Stadium, Wellington, on Saturday 18 September.
The All Blacks then head to Dunedin for the 100th Test between the All Blacks and South Africa at Forsyth Barr Stadium on Saturday 25 September with the team's final Rugby Championship Test against South Africa at Eden Park on Saturday 2 October.
Foster said the team was again looking forward to playing the Pumas and relishing the return of the Springboks to the Rugby Championship.
"Having the South Africans back in the Championship is going to be exciting for everyone. We haven't played them since Rugby World Cup 2019 so there'll be a lot of anticipation about them, and the 100th Test match is going to be an extra special occasion."
The 36-strong squad is as follows: Age, Super Rugby club, provincial union and Test caps in brackets.
Asafo Aumua (24, Hurricanes / Wellington, 2)
Dane Coles (34, Hurricanes / Wellington, 76)
Codie Taylor (30, Crusaders / Canterbury, 58)
Nepo Laulala (29, Blues / Counties Manukau, 31)
Tyrel Lomax (25, Hurricanes / Tasman, 8)
Joe Moody (32, Crusaders / Canterbury, 50)
Angus Ta'avao (31, Chiefs / Auckland, 16)
Karl Tu'inukuafe (28, Blues / North Harbour, 18)
Ofa Tuungafasi (29, Blues / Auckland, 39)
Scott Barrett (27, Crusaders / Taranaki, 42)
Brodie Retallick (30, Chiefs / Hawke's Bay, 83)
Patrick Tuipulotu (28, Blues / Auckland, 38)
Tupou Vaa'i (21, Chiefs / Taranaki, 4)
Samuel Whitelock (32, Crusaders / Canterbury, 125) - captain
Ethan Blackadder (26, Crusaders / Tasman, 2)
Shannon Frizell (27, Highlanders / Tasman, 14)
Akira Ioane (26, Blues / Auckland, 4)
Luke Jacobson (24, Chiefs / Waikato, 5)
Dalton Papalii (23, Blues / Counties Manukau, 5)
Ardie Savea (27, Hurricanes / Wellington, 50)
Hoskins Sotutu (23, Blues / Counties Manukau, 6)
TJ Perenara (29, Hurricanes / Wellington, 69)
Aaron Smith (32, Highlanders / Manawatu, 99)
Brad Weber (30, Chiefs / Hawke's Bay, 9)
Beauden Barrett (30, Blues / Taranaki, 91)
Richie Mo'unga (27, Crusaders / Canterbury, 24)
Braydon Ennor (23, Crusaders / Canterbury, 1)
David Havili (26, Crusaders / Tasman, 5)
Rieko Ioane (24, Blues / Auckland, 37)
Anton Lienert-Brown (26, Chiefs / Waikato, 50)
Quinn Tupaea (22, Chiefs / Waikato, 1)
Jordie Barrett (24, Hurricanes / Taranaki, 25)
George Bridge (26, Crusaders / Canterbury, 12)
Will Jordan (22, Crusaders / Tasman, 5)
Damian McKenzie (26, Chiefs / Waikato, 30)
Sevu Reece (23, Crusaders / Tasman, 10)