The Queensland Reds flanker takes over from Will Skelton, who skippered them during their disastrous Rugby World Cup campaign under Eddie Jones last year.
Skelton is based overseas and was not considered for the two-Test series against the Welsh, starting in Sydney on Saturday.
Whether Wright, who has played five Tests and none since 2020, is the long-term choice remains to be seen -- there have been six other captains in the space of a year.
Allan Alaalatoa and Tate McDermott, who both start from the bench, were also seen as in the running to don the armband, as was Dave Porecki who is injured.
"I think with Liam he's really understated. He's a leader in a Super Rugby team anyway so he's got that leadership experience," Schmidt said in explaining the choice.
"He was identified by the players as a natural leader in the group."
Schmidt took control in January with a big task ahead after Jones acrimoniously quit just 10 months into a five-year contract, having won just two from nine Tests.
That included a humiliating 40-6 flogging by Wales at the World Cup.
The fresh start will see Western Force lock Jeremy Williams and Queensland Reds' centre Josh Flook make their debut, with five more uncapped players on the bench, including Tom Lynagh, son of Wallabies legend Michael Lynagh.
Multiple stars snubbed by Jones for the World Cup return, with Jake Gordon and Noah Lolesio at scrum-half and fly-half respectively, Hunter Paisami at inside centre, Filipo Daugunu on the wing and Tom Wright at fullback.
"The squad has worked hard over the last week or so to prepare as best we can for what's going to be an incredibly tough Test against Wales," said Schmidt.
Great challenge
Since their big win over Australia at the World Cup, Wales have bid farewell to a host of experienced players and armed with a new squad failed to win a game at the Six Nations.
In a bid to get back on track, Wales coach Warren Gatland picked Gloucester winger Josh Hathaway to make his debut alongside Rio Dyer and 90-cap veteran Liam Williams at fullback.
He also named Ben Thomas at fly-half for his first appearance since 2021 despite playing most of his rugby at centre for Cardiff this year.
Archie Griffin will make his first senior start at tighthead prop, while Christ Tshiunza will feature for the first time since the World Cup, partnering Dafydd Jenkins in the second row.
"We've had a good week of preparations here in Sydney and are excited to get out on field on Saturday," said Gatland.
"This first Test is going to be a great challenge for us. Test matches are all about fine margins and we know we need to be accurate, keep our discipline and stay in the fight for the full 80 minutes."
They arrived in Australia without wing Keelan Giles, hooker Elliot Dee and flanker Jac Morgan who are all out injured. Tighthead props Keiron Assiratti and Henry Thomas are also missing.
Australia (15-1):
Tom Wright; Andrew Kellaway, Josh Flook, Hunter Paisami, Filipo Daugunu; Noah Lolesio, Jake Gordon; Rob Valetini, Fraser McReight, Liam Wright (capt); Lukhan Salakaia-Loto, Jeremy Williams; Taniela Tupou, Matt Faessler, James Slipper
Replacements: Billy Pollard, Issac Kailea, Allan Alaalatoa, Angus Blyth, Charlie Cale, Tate McDermott, Tom Lynagh, Dylan Pietsch
Wales (15-1)
Liam Williams; Josh Hathaway, Owen Watkin, Mason Grady, Rio Dyer; Ben Thomas, Ellis Bevan; Aaron Wainwright, Tommy Reffell, Taine Plumtree; Dafydd Jenkins, Christ Tshiunza; Archie Griffin, Dewi Lake (capt), Gareth Thomas
Replacements: Evan Lloyd, Kemsley Mathias, Harri O'Connor, Cory Hill, James Botham, Kieran Hardy, Sam Costelow, Nick Tompkins
