Dwyer, who led Australia to the trophy in 1991, told the Sunday Independent that he has been impressed with the Boks' improvement over the last 12 months and they have what it takes to be crowned world champions at the end of October.
"I have to say that for me, South Africa has absolutely improved out of sight in the last 12 months," he said.
"A year or more ago, their execution of almost everything was completely incorrect. Okay, their set plays were pretty good, but not a lot else was.
"Their catch-and-pass skills, running lines and support work at the breakdown were, in almost every instance, incorrect. It was their phenomenal physical superiority that kept them in the hunt.
"This year, there has been a big change in the Springboks' game.
"I don't know how it has happened. But take the Springboks' support lines at the tackle contest; they used to be so flat that the guy trying to transfer the ball was forced to transfer it like it was coming from a cannon.
"But things like that, and so many others, have changed. They're playing a lot, lot better."
Dwyer believes the Boks now have the firepower to win the tournament.
"I think they could win the World Cup," he said. "But to do that, they need all their best players to be fit and firing. The big problem is, they are a bit short of a fly-half. Butch James is not the perfect answer, but he is okay.
"But they have two very good centres in Jean de Villiers and Jacque Fourie.
"The key thing is not the individuals, but the strategy. And they have somehow developed very good running lines. They are also good at maintaining what little depth you need.
"The disadvantage of being flat in a backline is that it's very easy to become too flat. Now I see them playing tight off the edge of the maul and putting two or three passes together, which is very good.