"I like what he's doing," Henry told Newstalk ZB about Cheika. "I think we are seeing discipline within the group for the first time for quite some time. We are not getting the stories we were getting one year ago, two years ago about various players in the Australia team not towing the line and putting the team first. He's got the discipline and culture back in the group.
"Stephen Moore is an old-fashioned captain. He leads from the front and is respected by his troops. He's old school and expects people to do the business.
"The have gone from six in the world to two in the world in the last three or four months. They will be good and I think they will keep on getting better."
He added: "I think they could well be finalists."
Henry saw two areas that could jeopardise their campaign.
"Their two challenges are going to be goal kicking and who is going to play in the halves. They have had [Quade] Cooper and Bernard Foley but every time Matt Toomua player at 10 I think he looks the business. He's a very direct player.
"I would play [Will] Genia and Toomua at 9 and 10 but nobody else thinks that.
"But I don't know is anyone can kick goals. I don't know how good Toomua is as a goalkicker and I wonder if Matt Giteau will be in the top 15. If he is, he can goal kick a bit but he's no Daniel Carter."
One area Henry has been impressed with is Australia's improving forward pack, who are coached by Mario Ledesma, the former Argentine hooker who played 84 tests for Los Pumas.
"He's changed that pack," Henry said. "Now they have some stability at scrum time. When they played the All Blacks at Eden Park recently the thing I was surprised about was the foundation at scrum time that Ledesma has brought to this team.
"That was their Achilles heel. They were laughable at scrum time and it cost them test matches, particularly in the Northern Hemisphere. Now they have parity there and are using some ball from scrums."
Keep up with the latest Rugby World Cup news by signing up to the daily NZ Herald Sport newsletter.
Henry, who coached the All Blacks to the World Cup in 2011, refused to get drawn into a debate about comments this week from former England and Lions coach Clive Woodward that France would have won the final if it had been "refereed properly". The All Blacks clung on to win 8-7 and claim a first World Cup since 1987.
"I saw the headline of that [story] and just moved on the next section of the paper," Henry said. "I didn't read it.
"I take it with a grain of salt. It's history now and we need to move on. Clive was obviously pretty motivated to go down that angle and I don't know why. It will make no difference."
