McDermott, 24, will become the 86th Wallabies skipper when he leads Australia into battle in Dunedin, heading a starting team with few changes after the 38-7 loss in the Bledisloe opener at the MCG last Saturday.
He takes over the captaincy from Allan Alaalatoa who suffered a ruptured Achilles in that match.
"Tate's got all the attributes to be a great captain of his country and there's no doubt it will be a proud moment for him and his family when he leads the team on Saturday," Jones said.
Pone Fa'amausili will earn a first test start, named at tighthead prop in place of Alalaatoa with Taniela Tupou also unavailable through injury.
Richie Arnold comes into the starting team at lock alongside Nick Frost with Will Skelton dropping to the bench while Fraser McReight is introduced as openside flanker and Tom Hooper shifts to the blindside.
Jones has named an unchanged backline but overall, the starting XV has just 277 caps - the seventh-lowest total in the professional era.
Wallabies team:
Angus Bell, David Porecki, Pone Fa'amausili, Nick Frost, Richie Arnold, Tom Hooper, Fraser McReight, Rob Valetini, Tate McDermott (c), Carter Gordon, Marika Koroibete, Samu Kerevi, Jordan Petaia, Mark Nawaqanitawase, Andrew Kellaway. Reserves: Jordan Uelese, James Slipper, Zane Nonggorr, Will Skelton, Rob Leota, Nic White, Quade Cooper, Izaia Perese.
