Barrett, who has played 130 Tests, was dropped from the starting side for the defeat to South Africa in Cape Town. He comes in at full-back against the Wallabies in Sydney on Saturday, replacing Will Jordan who switches to the wing.
Loose-head prop Ethan de Groot has recovered from a neck injury to take the place of Tamaiti Williams, who drops to the bench. On the wing, Caleb Clarke takes over from Mark Tele'a, who misses out on the matchday squad.
The back three combination of Barrett, Jordan and Clarke ran riot when the All Blacks thrashed Argentina 42-10 in Auckland last month.
"We have selected an experienced team which has combinations that have played some of our best rugby this season," Robertson said in a statement.
The All Blacks boss is under pressure with New Zealand having won just one of their last four games, losing both Tests in South Africa after a shock home defeat in Wellington against Argentina last month.
The three defeats mean New Zealand are out of contention to retain the championship title with the Springboks top of the table.
Australia are bottom after also losing three of their four matches. After the Test in Sydney, Australia travel to face the All Blacks in Wellington a week later.
The teams will play for the Bledisloe Cup, which New Zealand has held since 2003, in the back-to-back matches.
"The Bledisloe Cup is so revered by both of these teams, we are expecting a classic showdown against our Australian rivals," Robertson added.
All Blacks replacement full-back Ruben Love has been ruled out of both Tests against the Wallabies with a quadricep injury. Prop Fletcher Newell is sidelined by a calf strain.
Australia will name their team later Thursday.
New Zealand: 15 Beauden Barrett; 14 Will Jordan, 13 Rieko Ioane, 12 Jordie Barrett, 11 Caleb Clarke; 10 Damian McKenzie, 9 Cortez Ratima; 8 Ardie Savea, 7 Sam Cane, 6 Wallace Sititi; 5 Tupou Vaa'i, 4 Scott Barrett (capt); 3 Tyrel Lomax, 2 Codie Taylor, 1 Ethan de Groot
Replacements: 16 Asafo Aumua, 17 Tamaiti Williams, 18 Pasilio Tosi, 19 Sam Darry, 20 Luke Jacobson, 21 TJ Perenara, 22 Anton Lienert-Brown, 23 Sevu Reece
