Among four changes from the side that lost its second Rugby Championship clash against the Springboks, Barrett will start at fullback at Accor Stadium on Saturday.
Clarke has recovered from a back injury to take his place on the left wing, with Jordan on the right wing.
In the forwards, Ethan de Groot will return from a neck injury to start at loosehead prop, while Pasilio Tosi will prepare to play just his second All Blacks Test match, having debuted off the bench against Fiji in San Diego earlier in the season.
"We have selected an experienced team which has combinations that have played some of our best rugby this season," All Blacks head coach Scott Robertson said on Thursday.
"The Bledisloe Cup is so revered by both of these teams, we are expecting a classic showdown against our Australian rivals.
"We have acknowledged the rich history of the Cup this week as a team and recognise that history does not bestow any rights.
"The Bledisloe Cup is always hard-earned and each year is its own chapter in the Bledisloe story."
The Wallabies must beat the All Blacks in Sydney for the first time since 2015 to stop the Bledisloe staying in New Zealand for a 22nd straight year.
The second Test will be played in Wellington on Saturday week.
All Blacks: Ethan de Groot, Codie Taylor, Tyrel Lomax, Scott Barrett (capt), Tupou Vaa'i, Wallace Sititi, Sam Cane, Ardie Savea, Cortez Ratima, Damian McKenzie, Caleb Clarke, Jordie Barrett, Rieko Ioane, Will Jordan, Beauden Barrett. Res: Asafo Aumua, Tamaiti Williams, Pasilio Tosi, Sam Darry, Luke Jacobson, TJ Perenara, Anton Lienert-Brown, Sevu Reece.
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