Prop James Slipper, who has stood in as captain in Hooper's place, will continue to lead the side for tests against Scotland, France, Italy, Ireland and Wales.
Australia coach Dave Rennie said he was delighted to have Hooper back in the squad and would not rule out a return to the captaincy for the 121-test openside flanker at some point in the future.
"It's great news from our perspective, he's really excited about travelling and playing," New Zealander Rennie told reporters.
"We just want him focusing on himself at the moment. Hoops's job is just to come in and just play well but he'll contribute massively in our leadership group as well.
"We'll assess things as we go."
The under-pressure Rennie named a much-changed 36-man squad for the tour after the Wallabies finished the Rugby Championship with back-to-back defeats against New Zealand.
Rennie recalled France-based lock Will Skelton and included lock Ned Hanigan in his first Wallabies squad since 2020 after he impressed in Japan for the Australia 'A' side.
Along with Skelton, Bernard Foley is the other overseas-based player included in the squad although the flyhalf will return to his Japanese club before the Wales game.
Rennie is restricted to picking only three overseas-based players per tour or series as part of Rugby Australia's selection policy.
Wallabies winger Marika Koroibete and lock Rory Arnold, both overseas picks this season, were unavailable because of Japanese club duties.
There was no place for veteran utility back Kurtley Beale or Fiji-born winger Suliasi Vunivalu.
"KB was a tough call in the end, we just want to make sure his body is right," Rennie said of 33-year-old Beale.
"He was close but we want him to have a good off season and then a big Super Rugby season."
Rennie selected five uncapped players with flyhalf Ben Donaldson, loose forward Langi Gleeson, winger Mark Nawaqanitawase and fullback Jock Campbell all included after impressing for Australia 'A'.
Squad:
Forwards - Allan Alaalatoa, Folau Fainga'a, Nick Frost, Matt Gibbon, Langi Gleeson, Ned Hanigan, Jed Holloway, Michael Hooper, Lachlan Lonergan, Fraser McReight, Cadeyrn Neville, Matt Philip, Dave Porecki, Tom Robertson, Pete Samu, Will Skelton, James Slipper, Sam Talakai, Taniela Tupou, Rob Valetini.
Backs - Tom Banks, Jock Campbell, Ben Donaldson, Lalakai Foketi, Bernard Foley, Jake Gordon, Reece Hodge, Len Ikitau, Andrew Kellaway, Noah Lolesio, Tate McDermott, Mark Nawaqanitawase, Hunter Paisami, Jordan Petaia, Nic White, Tom Wright
