Hooper will lead Michael Cheika's team into back-to-back tests against the world champion All Blacks when the southern hemisphere's Rugby Championship kicks off later this month.
The abrasive back-rower has long been groomed to step up to the role, having led the side throughout the 2014 season when Moore was injured.
Then, as a raw 22-year-old, he became the youngest player after Ken Catchpole to captain the Wallabies and guided the team to a whitewash victory over France in his first series in charge.
Now 25, Hooper has 68 tests to his credit and played a key role in Australia's run to the 2015 World Cup final when he and fellow openside flanker David Pocock teamed up in a powerful back row combination.
"It's a huge honour to just wear the Wallabies jersey, let alone captain the side," Hooper said in a statement on Wednesday.
"I'm extremely grateful to Cheik (Michael Cheika) but also to Steve (Moore) for all that he's done for me and the team.
"It's what you do in the jersey that's most important and I get another crack at showing what it means to me against New Zealand in Sydney in a fortnight.
"I'm really excited about what we can achieve in the next four months. It is a very special opportunity for all of us, and we'll be doing all we can to show that pride in the jersey."
Hooper will lead a rebuilding team during a tough period for Australian rugby and faces a baptism of fire against an All Blacks side smarting from being held to a draw in their recent series against the British and Irish Lions.
Australia's provincial teams were unable to win a single match against New Zealand opponents during the Super Rugby season, while the Wallabies drew scathing criticism for their performances during the June internationals.
After overcoming Fiji, they lost at home to Scotland and suffered a huge scare against lowly Italy.
Hooper's fitness to captain the Wallabies will also be questioned in some quarters, with former skipper and world class flanker Pocock set to return to the national setup next year after taking a year-long sabbatical.
Pocock could put pressure on Hooper's hold over the starting number seven jersey and is seen by some pundits as the ideal man to lead the Wallabies to the 2019 World Cup in Japan.
Hooper's leadership has also been queried after a difficult season at provincial level, with the New South Wales Waratahs slumping to their worst Super Rugby season in a decade under his captaincy.
Cheika has remained a staunch supporter, however, and said his record spoke for itself.
"Michael always shows on the field how much he loves the gold jersey and that's why he is totally respected among the rugby players in Australia.
"His role as the leader of this team will also be about making the standards of the Australian rugby team the highest they can possibly be."