Captain Michael Hooper leads the expanded 35-man squad but experienced utility back Reece Hodge misses out.
Playmaker Kurtley Beale, back in the international picture after returning to Australia following a spell in France, is injured and also misses out.
The series begins in Perth on 2 July.
Winger Vunivala switched to Queensland Reds in 2019 following a successful league career with Melbourne Storm.
"We picked him because of his massive potential," Wallabies coach Dave Rennie said.
Melbourne Rebels tighthead prop Pone Fa'amausili, ACT Brumbies locks Nick Frost and Cadeyrn Neville, New South Wales Waratahs lock Jed Holloway and his club team-mate, hooker Dave Porecki, are the other uncapped players selected.
Fly-half Quade Cooper and Fiji-born backs Samu Kerevi and Marika Koroibete, who all play in Japan, had earlier been announced as the three overseas picks allowed under Rugby Australia rules.
Melbourne Rebels' Hodge missed out because of "mixed form", Rennie explained, while another absentee, the in-form Western Force lock Izack Rodda, could be out for up to three months with a foot injury, he added.
Rennie said Waratahs' Beale needed to be carefully managed through a hamstring problem so he would be available for the Rugby Championship later this year.
Rennie said the series was the most important of his reign since taking on the role in 2019.
"I would say so," he said when asked.
"It's a big series and we're excited by it. We've spent so much time studying them and we know what's coming and our challenge is to be good enough to deal with that and apply pressure ourselves."