And while Tim Horan says it's a risk worth taking, the Wallabies great maintains only a semi-final appearance in France and further success beyond that will validate Rugby Australia's bold call.
Rennie was replaced on Monday in a shock move ahead of September's showpiece, Jones signing a five-year deal that also includes the women's Wallaroos job.
He had a Wallabies-worst 38 per cent win rate, compared to Jones' 73 per cent record when he was ousted from the England job in December.
The five-year deal would see Jones in charge for the British and Irish Lions' 2025 visit and a home World Cup in 2027.
"Eddie Jones as new Wallabies coach ... brave and has some risk," Horan tweeted.
"But maybe a risk worth taking considering the Wallabies current win/loss ratio.
"We need a Bledisloe Cup within two years and RWC semi and Lions win to justify the decision.
"Strap yourself in for the ride."
Rennie endured a terrible run of injury to key players and finished his tenure with a rousing comeback defeat of Wales.
But a consistent lack of discipline and poor record - the Wallabies slumped to No.8 in the world under Rennie - counted against the New Zealander.
RA chairman Hamish McLennan told AAP Jones' return would stimulate discussion around the team but also gift the side the best coach in the world that understands Australian rugby intricately.
"I feel for Rennie but at the same time if anyone can turn things around quickly it's Eddie," former Wallabies five-eighth Giteau tweeted.
"Some of the boys won't know what's hit them."
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