Hooper, 25, steps into the role immediately after Moore announced he would retire from Test rugby at the end of the season.
A veteran of 68 Tests, Hooper was confirmed as Moore's replacement on Wednesday.
"It's a huge honour to just wear the Wallabies jersey, let alone captain the side. I'm extremely grateful to Cheik [Wallabies coach Michael Cheika] but also to Steve for all that he's done for me and the team," Hooper said.
"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.
"There are quite a few good young leaders in this team like Bernard [Foley], Adam [Coleman], Samu [Kerevi] and Allan [Alaalatoa], so we'll be working together to take this team to a new level.
"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's first task as full-time skipper is a tough one – the Wallabies' Rugby Championship opener against New Zealand in Sydney on August 19.
The Waratahs man – a two-time John Eales Medallist – has captained Australia 15 times previously, including on 13 occasions in 2014.
"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," Cheika said.
"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.
"Michael loves Australia and his record as a player speaks for itself but he's exactly the type of man we want see in rugby – connected to his school, a great club man at the grassroots, a passionate Super Rugby player and a proud Wallaby."